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力學 | **力學**（英語：mechanics）是物理學的一個分支，主要研究能量和力以及它們與物體的平衡、變形或運動的關係。
## 發展歷史
人們在日常勞動中使用槓桿、打水器具等等，逐漸認識物體受力，及平衡的情況。古希臘時代阿基米德曾對槓桿平衡、物體重心位置、物體在水中受到的浮力等，作了系統研究，確定它們的基本規律，初步奠定了靜力學，即**平衡理論**的基礎，古希臘科學家亞里斯多德也提出**作用力造成運動**的主張，即物體不受力，必將停止。
自文藝復興之後，科學革命興起，伽利略的自由落體運動規律，以及牛頓的三大運動定律皆奠定了動力學的基礎。**力學**從此開始成為一門科學。此後彈性力學和流體力學基本方程的建立，使得力學逐漸脫離物理學而成獨立學科。到 20 世紀初，在流體力學和固體力學中，實際應用跟數學理論的互相結合，使力學勃起創立了許多新理論，同時也解決了工程技術中大量關鍵性問題。
## 古典力學及量子力學
力學主要可分為古典力學及量子力學。
若以發現的時間來看，古典力學較早被發現，啟源於牛頓的三大運動定律，量子力學則是 20 世紀初才由許多科學家所創立。
古典力學主要研究低速或靜止的宏觀物體。克卜勒、伽利略，尤其是牛頓是古典力學的奠基人。
量子力學應用範圍較廣，不過主要是針對微觀的物質。根據對應原理，量子數相當大的量子系統可以與古典力學中的行為模式相對應，使得量子力學及古典力學不會相衝突。量子力學可以解釋及預測分子、原子及基本粒子的許多行為。不過針對一般常見的巨觀系統，若使用量子力學會複雜到無法處理粒子間的交互作用，因此，巨觀系統透過古典力學的方式處理仍較為恰當。
## 相對論及牛頓力學
量子力學將力學延伸到古典力學以外的範圍，而愛因斯坦的廣義相對論及狹義相對論也將原來牛頓及伽利略的力學擴展到更大的範圍。在物體速度接近光速時，因相對論而產生的效應會主導物體的行為，也會使其速度不會超過光速。量子力學也需要配合相對論進行修正，量子場論就是量子力學和狹義相對論的結合。不過量子場論和廣義相對論目前仍無法整合，這是大一統理論希望可以克服的問題。
## 依研究物體來分類
在力學中，常用到一個名詞「物體」。物體可能是質點、拋體、太空船、星體、某些流體、某些固體、某些機械或某些土木建築。 | [
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力學 | 力學中的一些分支也和所探討的「物體」特性有關。例如質點就是小的物體，在古典力學中只視為一個有質量的點。而剛體有固定的大小及尺寸，不允許形變，和質點比較，剛體增加了一些稱為自由度的參數，例如在空間中的方向。
物體也有可能是可允許形變的半剛體，如彈性體，或者根本沒有固定的形狀，如流體。這些物體可利用古典力學的方式研究，也可以利用量子力學來分析。
例如一顆棒球的運動常使用古典力學來分析，而原子核內質子及中子的行為則通常會用量子力學來描述。
## 主要分支學科
在物理學的研究中，也有用「場」來描述物質的行為，稱為場論。其描述方式和力學使用的方式有些不同，可分為古典場論及量子場論。不過在實務上，場論及力學要探討的內容常常有密切的關係。例如作用在物體上的力常常是因為電磁場或重力場而產生，而當物體對其他物體產生作用力時，也常常會產生場。事實上，若以量子力學的觀點，物體也是場，可以用波函數來描述。
* 經典力學（基礎力學）
* 質點及剛體力學
* 應用力學或稱工程力學
* 靜力學
* 運動學
* 動力學
* 分析力學
* 拉格朗日力學
* 哈密頓力學
* 連續介質力學
* 固體力學
* 材料力學
* 彈性力學
* 塑性力學
* 損傷力學
* 接觸力學
* 斷裂力學
* 結構力學
* 土力學
* 流體力學
* 流體靜力學
* 流體動力學
* 空氣力學
* 水力學
* 生物力學
* 天體力學
## 參考來源
* 維基教科書：基礎力學 （頁面存檔備份，存於網際網路檔案館）
## 參見
* 力
## 延伸閱讀
## 外部連結
* iMechanica: the web of mechanics and mechanicians
* Mechanics Definition （頁面存檔備份，存於網際網路檔案館）
* Mechanics Blog by a Purdue University Professor （頁面存檔備份，存於網際網路檔案館）
* The Mechanics program at Virginia Tech | [
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力學 | * Physclips: Mechanics with animations and video clips from the University of New South Wales
* U.S. National Committee on Theoretical and Applied Mechanics （頁面存檔備份，存於網際網路檔案館）
* Interactive learning resources for teaching Mechanics
* The Archimedes Project
* Engineering Fundamental Solid & Fluid Mechanics （頁面存檔備份，存於網際網路檔案館） | [
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鋰 | **鋰**（拼音：lǐ，注音：ㄌ丨ˇ；英語：Lithium；源於拉丁語：λίθος，轉寫為「Lithos」，直譯「石頭」），是化學元素，化學符號 **Li**，原子序為 3，原子量為 6.941 u。中文名源於「_Lithos」_ 的第一音節發音「里」，而且是金屬，在左方加上部首「釒」。鋰是軟的銀白色鹼金屬。三粒電子中兩粒分布在 K 層，另一粒在 L 層。鋰是鹼金屬中最輕的一種。鋰常呈 + 1 或 0 氧化態，是否有 - 1 氧化態則尚未證實。但鋰和其化合物並不像其他的鹼金屬那麼典型，鋰的電荷密度很大並且有穩定的氦型雙電子層，使鋰易極化其他分子或離子，自己卻不易受到極化。這點影響到它和其化合物的穩定。
在標準條件，它是最輕的金屬和最輕的固體元素。同其他鹼金屬，鋰很活潑和易燃，應儲存在礦物油中。切割時展現出金屬光澤，但水氣會快速潮解之，變成暗銀灰色，接著變成黑色的氧化物。它不以元素狀態存在自然界，而只能於（通常是離子）偉晶岩礦物等化合物中出現，它們曾是鋰的主要來源。由於其離子的溶解度，它存在於海水中並通常從鹽水中獲得。從氯化鋰和氯化鉀的混合物中電解分離鋰金屬。
在自然界發現的兩種穩定同位素有所有穩定核素中每粒核子的結合能，鋰原子核處於不穩定狀態。核的性質相對不穩定，鋰在太陽系的含量排名第 26。由於以上因素，鋰在核物理學具重要用途。1932 年鋰原子向氦的核分裂是第一次完全人為的核反應，而氘化鋰用作熱核武器的燃料。
鋰及其化合物具多種工業用途，包括耐熱玻璃、陶瓷、鋰潤滑脂潤滑劑，用於生產鐵、鋼和鋁的助焊劑添加劑、鋰電池和鋰離子電池。這些用途消耗超過四分之三的鋰生產量。
在生物系統內有微量的鋰，但其功能不明。已知鋰鹽可作治療人類躁鬱症的情緒穩定藥物。
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鋰 | 1800 年，巴西化學及政治家若澤・博尼法西奧・德・安德拉達在瑞典烏托島的一個礦坑中發現透鋰長石（LiAlSi4O10）。不過直到 1817 年約翰・奧古斯特・阿韋德松（Johann Arfvedson）在化學家永斯・貝吉里斯（Jöns Jacob Berzelius）的實驗室中分析透鋰長石礦物時才發現這個新元素的存在。這個元素組成的化合物跟鈉和鉀的化合物相似，但其碳酸鹽和氫氧化物在水中的溶解性較小，鹼性也較低。貝采利烏斯將這個鹼金屬命名為「lithion／lithina」，來自希臘語單詞 λιθoς（音譯為 lithos，意為「石頭」），來反映它是在固體礦物中發現，而不是在植物灰燼中發現的鉀，或是部分因在動物血液中有高豐度而知名的鈉。他將材料中的金屬命名為「鋰」。阿韋德松後來發現，鋰輝石和鋰雲母礦物都有這種相同的元素。1818 年，Christian Gmelin 首次發現鋰鹽燃燒的焰色為鮮紅色，但阿韋德松和 Gmelin 都未能將純元素與其鹽分離。直到 1821 年威廉・托馬斯・布蘭德電解氧化鋰才得到元素鋰，而這一個過程過去曾被化學家漢弗里・戴維（Humphry Davy）用來分離鹼金屬鉀和鈉。布蘭德還描述了一些純鋰鹽，如氯化物，估計氧化鋰含有約 55％的金屬，並估計鋰的原子量大約為 9.8 克 / 莫耳（現代值約 6.94 克 / 莫耳）。1855 年，羅伯特・威廉・本生和 Augustus Matthiessen 電解氯化鋰生產了更多鋰。這程序發現後德國公司 Metallgesellschaft AG 於 1923 年藉電解熔融氯化鋰和氯化鉀的混合物在商業生產鋰。鋰的生產和使用歷史上經歷了幾次劇烈變化。 鋰的第一種主要用途是第二次世界大戰及之後不久用於飛機引擎的高溫鋰潤滑油脂及類似用途。這用途得到一些事實的支持：鋰基皂有比其他鹼皂更高的熔點，並且比鈣基皂有更低的腐蝕性。對鋰皂和潤滑脂的需求得到了幾家小型採礦企業的支持，其中大部分企業是在美國。隨著核熔合武器的生產，冷戰時期對鋰的需求急劇增加。當被中子照射時，鋰 6 和鋰 7 都會產生氚，可用於自身產生氚，以及在氫化鋰形式的氫彈內使用的一種固體聚變燃料。美國在 1950 年代末到 1980 年代中期之間成為鋰的主要生產國。最後，鋰儲存量約為 42000 噸氫氧化鋰 | [
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鋰 | 。儲存的鋰在鋰 6 中耗盡了 75％，這足以影響許多標準化學品中鋰的原子量，甚至一些「天然來源」中鋰的原子量已被從同位素分離設施排入地下水的鋰鹽污染。當使用霍爾－埃魯法工藝時，鋰用於降低玻璃的熔化溫度並改善氧化鋁的熔化行為。這兩種用途在 1990 年代中期佔據市場主導地位。核軍備競賽結束後，對鋰的需求下降，公開市場上能源庫存的出售進一步降低了價格。1990 年代中期，幾家公司開始從鹽水中提取鋰，比在地下或露天採礦更便宜。大多數礦山關閉或轉移到其他材料，因為只有來自分區偉晶岩的礦石才能以有競爭力的價格開採。例如，北卡羅來納州 Kings Mountain 附近的美國礦山在 21 世紀初之前關閉。 | [
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鋰 | 發展鋰離子電池增加了對鋰的需求，並在 2007 年成為主要用途。隨著 2000 年代鋰電池鋰需求激增，新公司擴大了鹽水開採工。有人認為，鋰在可再生能源和依賴電池的世界中將成為地緣政治競爭的主要對象之一，但這種觀點也被低估了經濟激勵對擴大生產的影響力。
## 存在與分布
### 天文上
雖然它在大爆炸中合成，但鋰（和鈹及硼）在宇宙中的含量明顯低於其他低原子序元素。破壞鋰所需的恆星溫度較低，以及缺乏常見生產鋰的過程。根據現代天文學，鋰的穩定同位素（鋰 6 和鋰 7）是三種在大霹靂產生的元素之一。雖然大爆炸核合成產生的鋰量取決於每粒重子的光子數，但有可接受的值，所以可以計算鋰豐度，而且宇宙中存在「宇宙學上的鋰差異」：老恆星的鋰含量似乎比應有的少，而一些年輕的恆星則有更多。老恆星中缺鋰顯然是由於鋰「混合」到恆星內部並被破壞，而鋰則在年輕恆星中產生。雖然它在高於攝氏 240 萬度（大多數恆星內部容易達到）時會因和質子碰撞而轉變為兩粒氦原子，但鋰含量仍比目前計算預測出在後代恆星中的要多。在棕矮星和某些異常的橙色恆星中也發現了鋰。鋰存在於較冷、質量較小的棕矮星中，但在較熱的紅矮星中被破壞，它在恆星光譜中的存在可用於「鋰試驗」，以區分皆比太陽小的棕矮星及紅矮星。某些橙色恆星也可能含有高濃度的鋰。那些有高於平均鋰濃度的橙色恆星（如 Centaurus X-4）繞著大質量的物體（中子星或黑洞）轉，它們的重力明顯將較重的鋰吸引到氫氦星的表面，導致我們觀測到更多的鋰。2015 年 2 月 19 日，日本國立天文台研究團隊從觀察 2013 年海豚座新星發現，新星爆炸製成了大量鋰元素，這意味著經典新星爆炸可能是宇宙製造鋰元素的主要機制。
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鋰 | 鋰在自然界豐度居第 27 位，地殼約含 0.0065%，儘管鋰在地球上廣泛分佈，但鋰活性高，在大自然不以元素形式存在。鋰的礦物有 30 餘種，主要在鋰輝石（ ${\ce {LiAlSi2O6}}$ ）、鋰雲母以及透鋰長石（ ${\ce {(LiNa)AlSi4O10}}$ ）和鋰蒙脫石黏土中。在人和動物的有機體、土壤和礦泉水、可可粉、菸葉、海藻中都有鋰存在。鋰在海水中的總含量非常大，估計為 2300 億噸，其中元素存在的相對恆定濃度為 0.14 至 0.25 百萬分之一濃度（ppm），或 25 微莫耳；而在海底熱泉附近，可以發現接近 7 ppm 的較高濃度。在地球，鋰含量估計占地殼重量的 20 至 70 ppm。鋰占火成岩的一小部分，其中在花崗岩中的濃度最大。花崗岩偉晶岩也提供最豐富的含鋰礦物，鋰輝石透鋰長石是商業上最可行的來源。另一種重要的鋰礦物來源是鋰雲母，它是由一系列的聚苯硫磷礦和三鋰鐵礦所形成，如今已成為一個過時的稱號。鋰的新來源是鋰蒙脫石黏土，目前只有美國的 Western Lithium 公司積極開發。在地殼中，鋰是第 25 位豐富的元素，每千克地殼含有 20 毫克的鋰。根據鋰和天然鈣的指南：「鋰是一種較稀有的元素，雖然它存在於許多岩石和一些鹽水中，但濃度總是非常低。鋰礦物和鹽水沉積物相當多，但是有實際或潛在的商業價值的，相對較少。很多價值非常小，其餘的則等級太低。」美國地質調查局估計，2010 年，智利擁有最大的儲量（目前 750 萬噸），而且年產量最高（8,800 噸）。鋰最大儲備基地位於玻利維亞的烏尤尼鹽沼地區，該地區有 540 萬噸。其他主要供應商包括澳大利亞、阿根廷和中國。截至 2015 年，捷克地質調查局將捷克共和國的整個厄爾士山脈視為鋰的礦區。註冊了五張礦床，其中一張靠近 Cínovec [cs] 的有 16 萬噸鋰，被認為是潛在的經濟礦床。 | [
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鋰 | 2010 年 6 月，紐約時報報導說，美國地質學家正在調查阿富汗西部乾鹽湖的地質，相信那裡有大量的鋰沉積物。五角大廈的官員表示，他們在一個位於加茲尼省的地方初步分析後，顯示此處與玻利維亞的鋰礦床潛力一樣大，而玻利維亞現今為世界上已知的最大鋰儲備地。這些預測主要根據舊數據，大部分在 1979－1989 年間被聚集，此時為蘇聯人佔領阿富汗的期間。美國地質調查局中阿富汗礦業項目的負責人史蒂芬・彼得斯說，過去兩年，他沒有意識到美國地質勘探局參與任何新的阿富汗礦產調查。他說：「我們不知道有任何鋰的發現。」鋰鹽水與英格蘭康瓦爾郡的錫礦區相關，目前考慮在 400 米深的測試鑽孔中評估項目。如果成功，熱鹽水的地熱能也將提供為鋰提取和精煉過程中的動力。按美國地質調查局推算，2016 年時鋰礦的世界蘊藏量 1400 萬噸，總生產量約 3 萬 5000 噸，其中智利的儲量達世界總儲量的 52%，中國 22% 居次，阿根廷和澳大利亞分別佔 14% 和 11%。生產方面澳大利亞通過礦石精製，南美洲則以費時的晾曬法提取鹽湖中鋰，所以前者生產效率比較高而生產量居世界之首，佔 41%，智利居次 34%，及阿根廷 16%、中國 6%。
### 生物上
在許多植物、浮游生物和無脊椎動物中能發現微量的鋰，濃度為 69 至 5760 ppb。在脊椎動物中，鋰濃度略低，幾乎所有脊椎動物組織和體液都含有 21 至 763 ppb 的鋰。海洋生物比陸地生物更容易將鋰生物累積。而鋰是否在這些生物體中有生理作用尚不清楚。
## 單質性質
### 概述
鋰是一種極易反應的柔軟的銀白色鹼金屬。它在金屬中比重最輕。鋰在空氣中易氧化，所以須貯存於固體石蠟、煤油或惰性氣體中。它能與水和酸作用放出氫氣，易與氧、氮、硫等化合。鋰鹽在水中的溶解度與鎂鹽類似，而不同於其他的鹼金屬鹽。
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鋰 | 就像其他鹼金屬一般，鋰有一粒價電子而易失去而形成陽離子，是熱和電的良導體且為極易反應的元素，但其價電子和原子核很近（剩下的兩粒電子在 1s 軌域中，能量低且不參與化學鍵結），故此在鹼金屬中反應性最低。然而，液態鋰的反應性較固態鋰高許多。鋰金屬性質柔軟，可用刀切開，在切開的同時，銀白色切面會快速氧化為灰色的氧化鋰。雖然鋰的熔點在金屬中甚低（180°C，453 K），但卻是鹼金族中熔點及沸點最高的元素。鋰金屬有極低密度（0.534 g/cm3）和松木相當，為所有固體元素在室溫下密度最低的，第二低的鈉（0.862 g/cm3）比它密度高 60% 以上。且除了氫和氦之外，固體鋰的密度比任何其他液體元素還低，只有液氮（0.808 g/cm3）的三分之二倍。 鋰可以漂浮於最輕的烴油，也是三種可在水上漂浮的金屬之一，另外兩種則是鈉和鉀。鋰的熱膨脹係數是鋁的兩倍也幾乎是鐵的四倍。在 400 μK 標準壓力下，或在較高溫度（9K 以上）極大壓力（20GPa 以上）下，鋰有超導現象。在 70K 以下時，鋰像鈉一樣有無擴散的相變發生。在 4.2K 時，晶體為六方晶系（九層重複堆積），溫度升高後轉變為面心結構，再變為體心結構。六方晶系在液氦溫度（4K）很常見。鋰也在高壓有多種同素異形體的結構。鋰的比熱容為 3.58KJ/kg-k，是所有固體中最高，常用來當作熱傳導應用的冷卻劑。
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鋰 | 鋰很易與水反應，但活性卻比其他鹼金屬小許多。該反應在水溶液中會形成氫氣和氫氧化鋰。通常會和固體石蠟一起存放在碳氫化合物構成的密封罐中。雖然其他更重的鹼金屬可以存放在密度更大的物質中，像是礦物油，但鋰密度太小，無法完好浸至這些物質之中。在潮濕的空氣之中，鋰會快速失去光澤，外表會形成黑色的氫氧化鋰（LiOH 和 LiOH・H2O）、氮化鋰（Li3N）和碳酸鋰（Li2CO3，LiOH 和 CO2 應的結果。）接近火時，鋰化合物會發出強烈的深紅色，然而當鋰燃燒很旺盛時，火焰會轉為銀白色的亮光。暴露在水或水蒸氣中時，氧氣會點燃鋰並燃燒。鋰是易燃的，暴露在空氣中尤其是水中，可能會爆炸，但可能性較其他鹼金屬低。在常溫，鋰和水反應是活潑但非劇烈，反應產生的氫通常不會自燃。鋰生成的火很難熄滅，鋰與所有鹼金屬都需要乾粉滅火器（D 類）。而在標準狀況下，鋰是少數能與氮反應的金屬。鋰與鎂有對角線規則，它們有相似的原子和離子半徑。而它們相似的化學性質包括，與氮氣反應形成氮化物，在氧氣中燃燒時形成氧化物 （Li2O）和過氧化物（Li2O2），有相似溶解度的鹽，以及碳酸鹽 和氮化物的熱不穩定性。 鋰在高溫下與氫氣反應生成氫化鋰（LiH）。其他已知的二元化合物包括鹵化物（氟化鋰 LiF、氯化鋰 LiCl、溴化鋰 LiBr、碘化鋰 LiI），硫化物（硫化鋰 Li2S），超氧化物（超氧化鋰 LiO2）和碳化物（碳化鋰 Li2C2）。而對於其他許多的無機化合物，鋰會與陰離子結合而形成鹽：硼酸鹽、醯胺、碳酸鋰、硝酸鋰或硼氫化物（硼氫化鋰 LiBH4）。氫化鋁鋰（LiAlH2）通常用作有機合成中的還原劑。氦化鋰是一種相互作用非常弱的凡德瓦化合物，已在非常低溫中檢測到。與第一族中其他元素不同的是，鋰的無機化合物遵循偶體法則，而不是八隅體法則。
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鋰 | 鋰在自然界以兩種同位素鋰 6 和鋰 7 組成，後者較豐富（在自然界豐度約 92.5%）。兩者皆有極低的核結合能（和在元素週期表中相鄰的元素：氦和鈹相比）。鋰是唯一低原子序元素中可藉核分裂產生淨能的元素。兩種鋰原子核皆有較低的束縛能，低於除了氘及氦 3 的其他穩定核素，因此，雖然它的原子量很小，在前 32 個元素中，鋰在太陽系中的含量低於其中的 25 個。 據目前所知，鋰有 7 個放射性同位素，最穩定的是半衰期 838 ms 的鋰 8 和半衰期 178 ms 的鋰 9，其他的放射性同位素半衰期皆少於 8.6ms ，半衰期最短的同位素為因質子發射後衰變的鋰 4，半衰期僅 7.6×10−23s。Li7 是產生於大霹靂核合成時的其中一種初始元素（或稱初始核素），少量鋰 6 和鋰 7 產生於恆星，可是被視為在出現同時又燒掉了，還有其他少量的鋰 6 和鋰 7 可能產生於太陽風、宇宙射線擊中較重的原子，和從早期太陽系的 7Be 和 10Be 的放射性衰變中產生。雖然鋰會產生於恆星核合成，但之後又會銷毀。鋰 7 也可以在碳星中產生。
鋰的同位素分餾基本上透過很多的自然過程，包含礦物形成（化學沉澱）、代謝和離子交換。鋰離子取代了八面體位置黏土礦物中的鎂和鐵，其中鋰 6 優於鋰 7 ，導致在超微過濾和岩石蝕變過程中富含輕同位素。已知外來的 11Li 會表現出核暈。雷射同位素分離的過程可用於分離鋰同位素，特別是鋰 7 與鋰 6。製造核武器和其他核物理用途是人工鋰分餾的主要來源，工業和軍事庫存保留了輕同位素鋰 6，其程度已使自然界的鋰 6 和鋰 7 比例在河流等地方有輕微但可測量出的變化。導致鋰標準化原子量異常不確定，因為它取決於這些自然界存在的穩定鋰同位素的自然豐度比例，它們可用於商業鋰礦物來源。鋰的兩種穩定同位素都可用雷射冷卻，並用於生產第一量子縮退玻色－費米混合物。
通過人工製備，已得到鋰的四種放射性同位素 ${\ce {^5Li}}$ 、 ${\ce {^8Li}}$ 、 ${\ce {^9Li}}$ 、 ${\ce {^11Li}}$ ，衰變方式如下：
: : ${}_{3}^{5}\mathrm {Li} \rightarrow {}_{1}^{1}\mathrm {H} +{}_{2}^{4}\mathrm {He} $
: ${}_{3}^{8}\mathrm {Li} \rightarrow \beta +{}_{4}^{8}\mathrm {Be} $ | [
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] |
鋰 | : ${}_{3}^{9}\mathrm {Li} \rightarrow \beta +{}_{4}^{9}\mathrm {Be} $
: ${}_{3}^{11}\mathrm {Li} \rightarrow \beta +{}_{4}^{11}\mathrm {Be} $
鋰的同位素可發生下列反應，放出熱量：
: : ${}_{3}^{6}\mathrm {Li} +{}_{1}^{3}\mathrm {H} \rightarrow 2\ {}_{2}^{4}\mathrm {He} +{}_{0}^{1}\mathrm {n} $
: ${}_{3}^{7}\mathrm {Li} +{}_{1}^{1}\mathrm {H} \rightarrow 2\ {}_{2}^{4}\mathrm {He} $
也可用來製備氚：
: : ${}_{3}^{6}\mathrm {Li} +{}_{0}^{1}\mathrm {n} \rightarrow {}_{1}^{3}\mathrm {H} +{}_{2}^{4}\mathrm {He} $
## 製備
### 鋰礦的提取法
#### 硫酸鹽法
鋰輝石和硫酸鉀一起燒結，鉀將鋰置換出來，形成可溶於水的硫酸鋰。
: 2LiAl(SiO3)2＋K2SO4 → Li2SO4＋2KAl(SiO3)2
硫酸鹽分解法很長一段時間內是工業製備鋰的唯一方法。此方法不僅適用於鋰輝石，也可用來處理鋰雲母。
#### 石灰法
將石灰或石灰石與鋰礦石一起燒結，然後用水處理，浸取液經多次蒸發，可從中結晶析出氫氧化鋰，反應式如下（溫度為 1000℃）：
: 2LiAl(SiO3)2＋9CaO → Li2O＋CaO·Al2O3＋4[2CaO·SiO2]
此方法的優點是：
1. 適用性強，能分解幾乎所有鋰礦石。
2. 反應不需要稀缺原料，石灰和石灰石均較便宜且容易獲得。
缺點是：
1. 燒結時精礦會貧化，精礦中鋰含量要求很高。
2. 浸取後得到的是稀溶液，蒸發會消耗大量熱量，且耗時長。
#### 硫酸法
首先提出此方法的是 R.B.Ellestad 和 K.M.Leute，此方法適用於 β- 鋰輝石和鋰雲母。原理如下（溫度為 250－300℃）：
: 2LiAl(SiO3)2＋H2SO4 → Li2SO4＋H2O·Al2O3·4SiO2 | [
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鋰 | 此反應的關鍵問題是硫酸只能與 β- 鋰輝石反應，而對於 α- 鋰輝石無法與之反應。用硫酸直接分解未經鍛燒的鋰輝石，提取出來的鋰僅占總量的 4%。
#### 天然滷水的提取
鋰的來源也包括天然滷水和某些鹽湖水。加工過程是將鋰沉澱成 Li2NaPO4，再將其轉變為碳酸鋰，即可作為原料來加工其他鋰化合物了。加工天然滷水還可得到硼砂、碳酸鉀、氯化鈉、硫酸鈉和氯化鎂等。
### 金屬鋰的製備
#### 電解法
鋰可由電解熔融氯化鋰而得。Guntz 首先建議用電解熔融氯化鋰和氯化鉀的混合物來製備金屬鋰，這樣可以把熔融溫度從單質鋰的 610℃降至 400℃。以石墨為陽極，以低碳鋼為陰極，電解槽壓為 6.0－6.5V。這樣可以得到純度達到 99% 的鋰。
: ${\ce {Li+ + e- -> Li}}$
: ${\ce {2Cl- -> Cl2 + 2e-}}$
: 2LiCl(l) → 2Li(s)＋Cl2(g)
電解法製得的金屬鋰通常有 Na、K、Mg、Ca、Fe、Si 和 Al 等機械雜質，須提純；雜質可重新熔融，再藉助比重不同濾除，不易除去的鈉和鉀可以通過氫化法除去。
#### 熱還原法
3Li2O＋2Al → 6Li＋Al2O3—33.6 千卡
2Li2O＋Si → 4Li＋SiO2—76.3 千卡
還原氧化鋰是吸熱反應，再加上金屬鋰性質十分活潑，只能在高溫和高真空中反應。
## 用途
### 合成原料
鋰在許多反應可作為原料或中間物。在合成與鋰相關的無機化合物時，常常是將金屬鋰與其他單質反應。若要求純度較高，可用鋰與氣態單質或化合物反應。例如用鋰和硫化氫合成硫化鋰。反應方程式如下：
: 2Li + H2S → Li2S + H2
### 還原劑
金屬鋰溶於液氨和乙醇的混合溶劑中形成良好的還原劑，可用來還原含芳香環的有機化合物。貴重的甾化合物通常用這種辦法來還原。此法的優點是產率較高，缺點是比用鈉還原昂貴，所以僅用於還原一些貴重的化合物。
### 催化劑
鋰可用作丁二烯、異戊二烯等二烯烴聚合催化劑，也可用來製造共聚物。
### 電池工業
鋰的原子量很小，只有 6.9g・mol−1，用作陽極的電池有很高的能量密度。鋰也能製造用於低溫或高溫的電池。 | [
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鋰 | 用於低溫的電池通常用有機溶劑作電解質，並加入無機鹽使之更導電，常用無機鹽有高氯酸鋰、六氟磷酸鋰、六氟砷酸鋰和硫化鋰等。二次鋰電池中正極材料也為含鋰化合物，如鋰鈷氧化物、鋰鎳氧化物、鋰錳氧化物、鋰鐵氧化物等等，以及其多元化合物。二次鋰電池中負極材料，也與鋰的作用明顯。
: 電池陰極是鋰，陽極常用金屬氯化物。例如鋰－氯化銀電池的電池反應為：
: Li + AgCl → LiCl + Ag
用於高溫的電池，通常用熔融無機鹽作電解質，必須在該鹽的熔點以上方可使用。例如：
: 2Li + Cl2 → 2LiCl
### 合金
摻有鋰的合金一般有強度大，密度小，耐高溫等特性。也有人用鋰合成了鋰－鉛液態半導體合金。
### 醫療
醫療用途的鋰目前主要分為兩種：一種為外用的局部治療，另一種則為已廣泛使用的口服治療。.
根據臨床研究中顯示，當鋰使用於外用的局部治療時，能有效治療脂漏性皮膚炎（seborrheic dermatitis），目前鋰的作用機理還不十分清楚，這可能與鋰可抑制物質 - P（substance-P）及抑制 Malassezia yeasts（引發痘痘元兇之一的細菌）生長所需的所有游離脂肪酸有關。過去的一些研究顯示鋰可以抑制許多酶（enzyme）：鈉鉀泵（Na/K ATPase）、腺苷環化酶（adenylcyclase）、enzymes of the prostaglandins E1 synthesis、和 inositol-1-phosphatase 等。 鋰亦有抗發炎（anti-inflammatory）及免疫調節（immunomodulatory）的作用。除此之外，在法國的研究中顯示含鋰元素的活泉水（ Evaux thermal spring water）能改善癌症患者因治療所引起的皮膚指甲等的副作用。
口服的鋰主要用於精神科，用來治療躁鬱症。臨床使用的濃度為 1 毫克。口服用的鋰會造成許多皮膚的副作用，像是斑點丘疹（maculopapular eruption）、痤瘡（acne）、牛皮癬狀疹（psoriasiform eruption）。因此顯示口服的鋰有可能會促進或使已經存在的皮膚疾病更惡化，像是牛皮癬（psoriasis）和脂漏性皮膚炎（seborrheic dermatitis）。
### 其他用途
鋰還能用於：
1. 原子能工業中製造核反應爐的載熱劑
2. 製造特種合金、特種玻璃等 | [
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] |
鋰 | 3. 作冶金工業中的脫氧劑，脫硫劑和脫泡劑
4. 作為燃料，可發射魚雷等武器
5. 可作為煙火的紅色部分
### 保存方法
乾燥環境下，鋰金屬不與氧氣發生反應，只有在潮濕的環境下才與氧氣發生反應，顏色由銀白色變成黑色最後再變成白色。實驗室中鋰金屬一般保存在乾燥的惰性氣體環境或是煤油中。
## 註解
## 參考資料
## 外部連結
* 元素鋰在洛斯阿拉莫斯國家實驗室的介紹（英文）
* EnvironmentalChemistry.com —— 鋰（英文）
* 元素鋰在 _The Periodic Table of Videos_（諾丁漢大學）的介紹（英文）
* 元素鋰在 Peter van der Krogt elements site 的介紹（英文）
* WebElements.com – 鋰（英文）
* 青海經濟信息網：自然資源（鹽類礦產 —— 鋰礦）
* 鋰與社會 | [
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機械工程 | **機械工程**（英語：Mechanical engineering）是一門涉及利用物理定律為機械系統作分析、設計、生產及維修的工程學科。
機械工程是眾多工程學科中範圍最廣的一科。任何現代產業和工程領域都需要應用機械，例如：農業、林業、礦業等需要農業機械、 林業機械、礦業機械；冶金工程和化學工程需要冶金機械、化工機械；紡織和食品加工業需要紡織機械、食品加工機械；水利、土木建築、道路和橋梁等工程需要工程機械；電力工程需要電力機械；交通運輸業需要各種車輛、船舶、飛機等；各種商品的計量、包裝、儲存、裝卸需要各種相應的工作機械。
各個工程領域的發展都要求機械工程有與之相適應的發展，都需要機械工程提供所必需的機械。某些機械的發明和完善，又導致新的工程技術和新的產業的出現和發展，例如：大型機械的成功製造，促成了電力系統的建立；火車的發明導致了鐵路工程和鐵路事業的興起；內燃機、燃氣輪機、火箭發動機等的發明和進步以及船舶、飛機和航空器的研製成功導致了航海工程、航海事業、航空工程和航空事業的興起；高壓設備（包括壓縮機、反應器、密封技術等）的發展導致了許多新型合成化學工程的成功。機械工程就是在各方面不斷提高的需求的壓力下獲得發展動力，同時又從各個學科和技術的進步中得到改進和創新能力。
## 發展演進歷史
### 古代
人類成為「現代人」的標誌是製造工具。石器時代的各種石斧、石錘、木弓和木質、皮質的簡單粗糙的工具是後來出現的機械的先驅。從製造簡單工具演進到製造由多個零件、部件組成的現代機械，經歷了漫長的過程。
幾千年前，人類已創製了例如用於穀物脫殼和粉碎的臼和磨，用來提水的桔槔和轆轤，裝有輪子的車，航行於江河的船及其槳、櫓、舵等。所用的動力，從人自身的體力，發展到利用畜力、風力和水力。所用材料從天然的石、土、木、皮革，發展到人造材料。最早的人造材料是陶瓷。製造陶瓷器皿的陶車，已是具有動力、傳動和工作三個部分的完整機械。
人類從石器時代進入銅器時代，再進而到鐵器時代，用以吹旺爐火的鼓風器的發展起了重要作用。有足夠強大的鼓風器，才能使冶金爐獲得足夠高的爐溫，才能從礦石中煉得金屬。在中國公元前 1,000～前 900 年就已有了冶鑄用的鼓風器，並漸從人力鼓風發展到畜力和水力鼓風。 | [
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機械工程 | 早在公元前，中國已在指南車上應用複雜的齒輪系統，在被中香爐中應用了能永保水平位置的十字轉架等機件。古希臘已有圓柱齒輪、圓錐齒輪和蝸杆傳動的記載。但是關於齒輪傳動瞬時速比與齒形的關係、齒形曲線的選擇，直到 17 世紀之後方有理論闡述。手搖把和踏板機構是曲柄連杆機構的先驅，在各文明古國都有悠久歷史，但是曲柄連杆機構的形式、運動和動力的確切分析和綜合，則是近代機械學的成就。
機械學作為一個專門學科遲至 19 世紀初才第一次列入高等工程學院（巴黎的工程學院）的課程。通過理論研究，人們方能精確地分析各種機械，包括複雜的空間連杆機構的運動，並進而能按需要綜合出新的機構。
### 近代
15－16 世紀以前，機械工程發展緩慢。但在以千年計的實踐中，在機械發展方面還是積累了相當多的經驗和技術知識，成為後來機械工程發展的重要潛力。17 世紀以後，資本主義在英、法和西歐諸國出現，商品生產開始成為社會的中心問題。許多高才藝的機械匠師和有生產觀念的知識分子致力於改進各產業所需的工作機械和研製新的動力機械──蒸汽機。18 世紀後期，蒸汽機的應用從採礦業推廣到紡織、麵粉、冶金等行業。製作機械的主要材料逐漸從木材改用更為堅韌，但難以用手工加工的金屬。機械製造工業開始形成，並在幾十年中成為一個重要產業。機械工程通過不斷擴大的實踐，從分散性的、主要依賴匠師們個人才智和手藝的一種技藝，逐漸發展成為一門有理論指導的、系統的和獨立的工程技術。機械工程是促成 18－19 世紀的工業革命以及資本主義機械大量生產的主要技術因素。
#### 動力機械的發展
動力是發展生產的重要因素。17 世紀後期，隨著各種機械的改進和發展，隨著煤和金屬礦石的需要量的逐年增加，人們感到依靠人力和畜力不能將生產提高到一個新的階段。在英國，紡織、磨粉等產業越來越多地將工場設在河邊，利用水輪來驅動工作機械。但當時已有一定規模的煤礦、錫礦、鋁礦、鐵礦、銅礦、銀礦、金礦礦井中的地下水，仍只能用大量畜力來提昇和排除。
在這樣的生產需要下，18 世紀初出現了湯瑪斯・紐科門 (Thomas Newcomen) 的大氣式蒸汽機，用以驅動礦井排水泵。但是這種蒸汽機的燃料消耗率很高，基本上只應用於煤礦。
1765 年英國人瓦特發明了有分開的凝汽器的蒸汽機，降低了燃料消耗率。1781 年瓦特又創製出提供迴轉動力的蒸汽機，擴大了蒸汽機的應用範圍。蒸汽機的發明和發展，使礦業和工業生產、鐵路和航運都得以機械動力化。 | [
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機械工程 | 蒸汽機幾乎是 19 世紀唯一的動力源。但蒸汽機及其鍋爐、凝汽器、冷卻水系統等體積龐大、笨重，應用很不方便。19 世紀末，電力供應系統和電動機開始發展和推廣。20 世紀初，電動機已在工業生產中取代了蒸汽機，成為驅動各種工作機械的基本動力。生產的機械化已離不開電氣化，而電氣化則通過機械化才對生產發揮作用。
發電站初期應用蒸汽機為原動機。20 世紀初期，出現了高效率、高轉速、大功率的汽輪機，也出現了適應各種水力資源的大、小功率的水輪機，促進了電力供應系統的蓬勃發展。
19 世紀後期發明的內燃機經過逐年改進，成為輕而小、效率高、易於操縱、並可隨時啟動的原動機。它先被用以驅動沒有電力供應的陸上工作機械，以後又用於移動機械（如：拖拉機、堆高機、重機械）、車輛、飛機和船舶，到 20 世紀中期開始用於鐵路車輛。蒸汽機在汽輪機和內燃機的排擠下，已不再是重要的動力機械。內燃機和以後發明的燃氣渦輪發動機、噴氣發動機的發展，還是船舶、飛機、太空飛行器等成功發展的基礎技術因素之一。
#### 機械加工技術的發展
工業革命以前，機械大都是木結構的，由木工用手工製成。金屬（主要是銅、鐵）僅用以製造儀器、鎖、鐘錶、泵和木結構機械上的小型零件。金屬加工主要靠機匠的精工細作，以達到需要的精度。蒸汽機動力裝置的推廣，以及隨之出現的礦山、冶金、車輛、船舶、飛機等大型機械的發展，需要成形加工和切削加工的金屬零件越來越多，越來越大，要求的精度也越來越高。應用的金屬材料從銅、鐵發展到以鋼為主。機械加工包括鉗工、鑽床、車床、銑床、磨床、鋸床、沖床、刨床、模具、鑄造、鍛造、鈑金、焊接及熱處理等技術及其裝備，以及切削加工技術、刀具、量具等，得到迅速發展，保證了各產業發展生產所需的機械裝備的供應。
社會經濟的發展，對機械產品的需求猛增。生產批量的增大和精密加工技術的進展，促進了大量生產方法（零件互換性生產、專業分工和協作、流水加工線和流水裝配線等）的形成。
簡單的互換性零件和專業分工協作生產，在古代就已出現。在機械工程中，互換性最早體現在亨利・莫茲利於 1797 年利用其創製的螺紋車床所生產的螺栓和螺帽。同時期，美國工程師伊萊・惠特尼用互換性生產方法生產火槍，顯示了互換性的可行性和優越性。這種生產方法在美國逐漸推廣，形成了所謂「美國生產方法」。 | [
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機械工程 | 18 世紀以前，機械匠師全憑經驗、直覺和手藝進行機械製作，與科學幾乎不發生聯繫。到 18 世紀－19 世紀，在新興的資本主義經濟的促進下，掌握科學知識的人士開始注意生產，而直接進行生產的匠師則開始學習科學文化知識。他們之間的交流和互相啟發取得很大的成果。在這個過程中，逐漸形成一整套圍繞機械工程的基礎理論。
動力機械最先與當時的先進科學相結合。蒸汽機的發明人 T. 薩弗里、瓦特應用了物理學家 D. 帕潘和 J. 布萊克的理論。在蒸汽機實踐的基礎上，物理學家 S. 卡諾、W.J.M. 蘭金和開爾文建立起一門新的科學──熱力學。內燃機的最重要的理論基礎是法國的 A.E.B.de 羅沙在 1862 年創立的，1876 年尼古拉斯・奧托 (Nikolaus August Otto) 應用羅沙的理論，徹底改進了他原來創造的粗陋笨重、噪聲大、熱效率低的內燃機而奠定了內燃機的地位。其他如：汽輪機、燃氣輪機、水輪機等都在理論指導下得到發展，而理論也在實踐中得到改進和提高。
### 現代
在工業革命以前，大多數的工程項目都限於軍事及城市發展。從事軍事方面的工程師負責研製戰爭工具和系統；從事城市發展的工程師則負責建築和地面設施。在十九世紀早期的英國，機械工程師成為新興的行業，負責提供工業用機械和推動機械所需要的動力。在 1818 年，首個專業土木工程師組織成立，而機械工程師亦相繼於 1847 年成立組織。
20 世紀初期，福特，H. 在汽車製造上又創造了流水裝配線。大量生產技術加上泰勒，F.W. 在 19 世紀末創立的科學管理方法，使車輛和其他大量生產的機械產品的生產效率很快達到了過去無法想像的高度。
20 世紀中、後期，機械加工的主要特點是：不斷提高工具機的加工速度和精度，減少對手工技藝的依賴；發展少無切削加工工藝；提高成形加工、切削加工和裝配的機械化和自動化程度。自動化從機械控制的自動化發展到電氣控制的自動化和計算機程序控制的完全自動化，直至無人車間和無人工廠；利用數值控制工具機、加工中心、成組技術等，發展柔性加工系統，使中小批量、多品種生產的生產效率提高到近於大量生產的水平；研究和改進難加工的新型金屬和非金屬材料的成形和切削加工技術。
#### 機械工程師學會 | [
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機械工程 | 世界上建立最早的機械工程學術團體是英國機械工程師學會 IMechE，成立於 1847 年，第一任主席是鐵路機車發明家喬治・史蒂芬生。英國機械工程師學會的建立，標誌著機械工程已確立為一個獨立的學科，機械工程師被社會公認為受尊敬的職稱。
在此之前，從事機械製造、使用和修理的人，被稱為機器匠，社會地位不高。
隨著機械製造作為一個獨立的工業部門日益發展，各國機械工程師學會紛紛建立，這在很大程度上反映了機械工業初創階段，企業主和技術人員要求自由開展學術交流、維護共同利益、爭取提高社會地位的共同願望。
在西方，機械工程師學會和機械工程學科同時誕生，在推動學科發展、提高機械工程師社會地位方面起到了重要的作用。英國機械工程師學會根據國家法律規定，有權考核工程師，並授予特許工程師稱號。
德國工程師學會 (VDI) 成立於 1856 年，主要活動範圍是機械工程。它在制訂指導性技術文件方面在全國處於領先地位。美國機械工程師學會 (ASME) 成立於 1880 年。它承擔美國機械工業標準的制訂工作。日本機械工程師學會 (JSME) 成立於 1897 年。印度機械工程師學會 成立於 1920 年。中華民國機械工程學會成立於 1936 年。
各國機械工程師學會的主要活動大體相同，如組織學術討論會、協調科學研究任務、普及科學技術知識等。同時，各國的學會又根據各自社會和歷史背景的不同，發展各自的優勢，使各國的機械工程師學會又具有不同的特點。
在組織建制方面，各國機械工程學會經過不同的探索，一方面建立專業分會或專業委員會，開展專業性學術活動，另方面建立地區分支機構，組織地區性學術活動。這種組織結構逐步發展成為各國機械工程學會共同的特點和傳統。隨著機械化向各工業部門延伸，領域不斷擴大，各國機械工程學會多是歷史悠久、規模最大、會員最多、活動範圍最廣的學術團體。
20 世紀以來，特別是第二次世界大戰以來，各國機械工程學術團體有了大規模的發展。國際學術交流也日益頻繁。機械工程的一些專業分支學科，紛紛建立世界性統一的學術團體，例如：國際焊接學會 (IIW)、國際鑄造學會 (CIATF)、國際材料熱處理聯合會 (IFHT)、國際機器理論與機構學聯合會 (IFToMM)、國際壓力容器理事會 (ICPV)、國際無損檢測理事會 (ICNDT)、國際摩擦學理事會 (ITC)、國際生產工程研究會 (CIRP) 等。 | [
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機械工程 | 隨著機械工程學科各分支與相鄰專業學科互相滲透和綜合，還出現了一批國際性的工程學術團體，如 1950 年成立的國際技術協會聯盟 (UITA)、1958 年成立的世界工程組織聯合會等，參加的有近百個國家的工程組織，並取得聯合國教科文組織的支持。在這些國際工程組織中，機械工程學科和學術團體往往是一支中堅力量。
## 機械工程教育
機械工程是材料性質、應用力學、材料力學、熱力學、流體力學、結構力學、損傷力學（破壞力學）、彈性力學、塑性力學、電機電子及計算的理論，以設計及製造各類型的機械製品及系統，如：發動機、機器、儀器、消費品及機械、水力、熱力或熱傳系統。隨著科技的日新月異；電腦輔助製圖及電腦輔助製造技術已廣泛地被採用。一般來說，機械工程師會專注某一方面的工作，例如：水力、熱傳、熱機、電機電子、機電整合、控制系統，機器人製造、冷凍、冷藏、空氣調節、升降機與電梯，或某類特定的製品如：機器，推進系統、機器人及機動儀器等。
機械工程的工作對象是動態的機械，意即它的工作情況會發生很大的變化。這種變化有時是隨機的而不可預見；實際應用的材料也不完全均勻，可能存有各種缺陷；加工精度有一定的偏差等等。與以靜態結構為工作對象的土木工程相比，機械工程中各種問題更難以用理論精確解決。因此，早期的機械工程只運用簡單的理論概念，結合實踐經驗進行工作。設計計算多依靠經驗公式；為保證安全，都偏於保守。結果，製成的機械笨重而龐大，成本高、生產率低、能量消耗很大。
從 18 世紀起，設計計算從兩個方面不斷提高了精確度：在材料強度方面，從早期按靜強度除以安全係數（考慮一切不精確性和分散性因素的經驗係數）的粗糙計算，提高到考慮材料的疲勞（19 世紀後半期）；從一律按材料的無限疲勞壽命進行設計，改為按照實際要求的壽命進行有限壽命設計（20 世紀前半期）；從認為材料原則上不能有裂紋，發展到以斷裂力學理論為依據，考慮裂紋材料的強度和壽命。在結構力學分析方面，從應用經驗公式和簡化的力學分析來確定各種受力和力矩，發展到應用複雜的力學分析和數學計算方法。 | [
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機械工程 | 進入 20 世紀，又出現各種實驗應力分析方法。人們已能用實驗方法測出模型和實物上各部位的應力，在發現應力過高過低時，便可能作出必要的調整。20 世紀後半葉，人們開始應用有限元法和電子計算機的迅速可靠的數值計算，對複雜的機械及其零件、構件進行力、力矩、力偶、應力、應變等的分析和計算。對於掌握有充分的實踐或實驗資料的機械或其元件，已經可以運用統計技術，按照要求的可靠度科學地進行機械設計，或者按機械的實際情況（實際的質量、實際的使用條件等）科學地判斷其可靠度和壽命。但在許多機械工程工作中，仍還應用一些經驗方法、經驗公式和經驗係數等，不過其中的科學成分在不斷增加，經驗成分則不斷減少。
### 機械科系的專業化和綜合化
19 世紀時，**機械工程**的知識總量還很有限，在歐洲的大學院校中它通常還與水利工程、土木工程、建築工程綜合為一個學科，被稱為民用工程，19 世紀下半葉才逐漸成為一個獨立學科。
進入 20 世紀，隨著機械工程技術的發展和知識總量的增長，機械工程開始分解，陸續出現了專業化的分支學科。這種分解的趨勢在 20 世紀中期，即在第二次世界大戰結束的前後期間達到了最高峰。由於機械工程的知識總量已擴大到遠非一個人所能全部掌握，一定的專業化是必不可少的。
但是過度的專業化造成知識過分分割，視野狹窄，不能統觀和統籌稍大規模的工程的全貌和全局，並且縮小技術交流的範圍，阻礙新技術的出現和技術整體的進步，對外界條件變化（新技術、新材料和新產品的出現、新的環境保護法規、原材料和能源供應及價格的變動，以及個人的工作調動、職務提昇等）的適應能力很差
封閉性專業的專家們掌握的知識過狹，考慮問題過專，在協同工作時配合協調困難，也不利於繼續自學提高。因此自 20 世紀中、後期開始，又出現了綜合的趨勢。人們更多地注意了基礎理論，拓寬專業領域，合併分化過細的專業。
綜合→專業分化→再綜合的反復循環，是知識發展的合理的和必經的過程。但是，綜合的恢復，不能是現有專業的簡單合併，而是在更高一級上的綜合，其目的是為了能更好地發揮專業知識作用。不同專業的專家們各具有精湛的專業知識，又具有足夠的綜合知識來認識、理解其他學科的問題和工程整體的面貌，才能形成互相協同工作的有力集體。正確地而不是教條主義地處理知識的綜合與專業的關係，是新的技術革命時代中培養機械工程人才的主要課題。 | [
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] |
機械工程 | 綜合與專業是多層次的。在機械工程內部有綜合與專業的矛盾；在全面的工程技術中也同樣有綜合和專業問題。在人類的全部知識中，包括社會科學、自然科學和工程技術，也有處於更高一層、更宏觀的綜合與專業問題。
## 基礎學科
在美國，機械工程學的課程受到 ABET（頁面存檔備份，存於網際網路檔案館）的監管，以保證畢業生對有關項目有最起碼的認知。所以雖然各家院校所提供的課程內容有異，但一般的機械工程學課程都至少包含以下各個基本科目：
* 微積分 (Calculus)；
* 工程數學 (Engineering Mathematics)；
* 工程材料 (Engineering Materials)；
* 工程製圖 (Engineering Drawing)；
* 工程設計 (Engineering Design)；
* 工業工程 (Industrial Engineering)；
* 機械材料 (Mechanical Materials)；
* 機械製圖 (Mechanical Drawing)；
* 機械設計 (Mechanical Design)；
* 機械製造 (Mechanical Manufacturing)；
* 非傳統加工、特殊加工；
* 鑄造 (Casting)、鍛造 (Forging)、模具 (Mold)；
* 測量學、品管；
* 量度及儀器及儀表 (Instrumentation and Measurement)；
* 應用力學─靜力學及應用力學─動力學 (Mechanics of Applied-Statics and Mechanics of Applied-Dynamics)；
* 固體力學 (Mechanics of Solid)；
* 材料力學及材料強度學 (Mechanics of Materials and Strength of Materials)；
* 熱力學 (Thermodynamics)；
* 流體力學 (Mechanics of Fluid)；
* 損傷力學（破壞力學）(Mechanics of Damage)；
* 彈性力學 (Mechanics of Elasticity)；
* 塑性力學 (Ｍechanics of Plastic)；
* 機構學 (Kinematics of Machinery)；
* 液壓學 (Hydraulics)、氣壓學 (Pressure) 和氣動學 (Pneumatics)；
* 能量轉換； | [
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] |
機械工程 | * 熱傳遞、熱傳、熱處理、熱機、熱流；
* 冷卻及空氣調節；
* 電機、機電整合、自動控制、控制理論及微處理機；
* 電腦輔助設計 (CAD) 及電腦輔助製造 (CAM)；
* 固體塑模 (Modelling of Solid)
## 機械工程的服務領域和工作內容
### 服務領域
機械工程的服務領域廣闊而多面，凡是使用機械、工具，以至能源和材料生產的部門，無不需要機械工程的服務。概括說來，現代機械工程有五大服務領域。
* 研製和提供能量轉換機械，包括將天然機械能、聲能、光能、熱能、電能、磁能、化學能和流體壓力能轉換為適合於應用的機械能的各種動力機械，以及將機械能轉換為所需要的其他能量（機械能、聲能、光能、熱能、電能、磁能、化學能和流體壓力能等）的能量變換機械。
* 研製和提供用以生產各種產品的機械，包括應用於第一產業的農業、林業、牧業、漁業機械和礦山機械，以及應用於第二產業的各種重工業機械和輕工業機械。
* 研製和提供從事各種服務的機械，包括交通運輸機械（如：輪椅、慢車（自行車、獸力車）、車輛、飛機、船舶）、物料搬運機械（如：堆高機、起重機）、重機械（挖掘機、推土機、鏟裝機、裝載機）、辦公機械、醫療機器、通風、採暖和空調設備、除塵、淨化、消聲等環境保護設備等。
* 研製和提供家庭和個人生活中應用的機械，如：烤箱、咖啡機、縫紉機、洗衣機、脫水機、烘乾機、吹風機、電風扇、冰箱、冷氣、暖氣、熱水器、鐘錶、照相機、攝影機、錄影機、錄音機、收音機、電視機、電話機、手機、數據機、電腦、掃描機、列印機、印表機、事務機、傳真機、運動器材等。
* 研製和提供各種機械武器。
### 工作內容
不論服務於哪一領域，機械工程的工作內容基本相同，按其工作性質可分為六個方面。
* 建立和發展可以實際地和直接地應用於機械工程的工程理論基礎。這方面主要有：研究力和運動的工程力學、固體力學和流體力學；研究金屬和非金屬材料的性能及其應用的工程材料學；研究材料在外力作用下的應力、應變等的材料力學；研究熱能的產生、傳導和轉換的燃燒學、熱傳學和熱力學；研究摩擦、磨損和潤滑的摩擦學；研究機械中各構件間的相對運動的機構學；研究各類有獨立功能的機械元件的工作原理、結構、設計和計算的機械原理和機械零件學；研究金屬和非金屬的成形和切削加工的金屬工藝學和非金屬工藝學等。 | [
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] |
機械工程 | * 研究、設計和發展新的機械產品，不斷改進現有機械產品和生產新一代機械產品，以適應當前和將來的需要。這方面包括：調研和預測社會對機械產品的新的要求；探索應用機械工程和其他工程技術中出現的新理論、新技術、新材料、新工藝，進行必要的新產品試驗、試製、改進、評價、鑑定和定型；分析正在試用的和正式使用的機械存在的缺點、問題和失效情況，並尋求解決措施。
* 機械產品的生產。包括：生產設施的規劃和實現；生產計畫的制訂和生產調度；編制和貫徹製造工藝；設計、製造工具和模具；確定勞動定額和材料定額；組織加工、裝配、試車和包裝發運；對產品質量進行有效的控制。
* 機械製造企業的經營和管理。機械一般是由許多各有獨特的成形、加工過程的精密零件組裝而成的複雜的製品，生產批量有單件和小批，也有中批、大批，直至大量生產，銷售對象遍及全部產業和個人、家庭，而且銷售量在社會經濟狀況的影響下可能出現很大的波動。因此，機械製造商業的管理和經營特別複雜和困難。商業的生產管理、規劃和經營等的研究也多是肇始於機械工業。生產工程、工業工程等在成為獨立學科之前，都曾是機械工程的分支。
* 機械產品的應用。這方面包括選擇、訂購、驗收、安裝、調整、操作、維護、修理和改造各產業所使用的機械和成套機械裝備，以保證機械產品在長期使用中的可靠性和經濟性。
* 研究機械產品在製造過程中，尤其是在使用中所產生的環境污染和自然資源過度耗費方面的問題及其處理措施。這是現代機械工程的一項特別重要的任務，而且其重要性與日俱增。
### 機械工程人才
#### 科學家與學者
由於機械工程領域相當廣大，所以大多數的科學家與學者們多選擇精通機械領域的其中一門分支，並進行高深的基礎理論研究或者廣泛的應用科學研究。
#### 工程師
專業工程師必須具備邏輯思考、有系統地研究及分析問題的能力。由於機械工程的工作往往強調整體合作，工程師必須善於與人相處，並能明確闡述生產程序的安排。為配合科技的迅速發展，工程師須不斷進修，留意新科技如電腦輔助製圖╱電腦輔助製造的發展。常見職稱有：
* 1. 機械設計工程師
* 2. 機械製程工程師
* 3. 設備工程師
* 4. 研發工程師
* 5. 熱流工程師
* 6. 熱機工程師
* 7. 電機工程師
* 8. 伺服機構與控制工程師
#### 技術員 | [
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機械工程 | 由於技術員須明確掌握工程師的意念並付諸實行，他必須具備所需的技術知識。此外，他須有良好的判斷力及組織能力。擔任督導職務的技術員更須能激發其下屬工作，並清晰表達其指引。他亦應不斷進修最新的科技知識。
#### 技工
技工必須是務實及喜愛用手及工具製作物品的人。除具備基本的理論知識外，他亦須擁有其工作所需的實際技術。
### 薪酬及就業前景
隨著經濟日趨繁榮，製造及服務業均需求大量曾接受專門訓練的機械工程師及技術員。雖然新科技導致生產程序自動化及電腦化，但大部份與工業營運及儀器製作有關的程序，仍是以機械原理為依歸。鑒於各行業均朝著高科技的方向發展，相信各級機械技術人員的需求將繼續保持增長。
## 分支學科
機械工程可以看作是所有機械相關的集合。以下是機械工程系大部分的課程，附有簡短的解說和常見的應用說明。其中有些是機械工程才有的特色。機械工程師多是運用學自這些和其他更專業的課程的方法和技巧。其中應用力學（靜力學與動力學）、材料力學與流體力學為機械工程三大主角。更專業的課程是在研究所的課程。
* 結構分析或失效理論：機械工程領域的一個分支，它對於檢驗物體失效與否以及如何發生提供了貢獻。結構失效有兩種情況會發生：靜態失效、動態失效與疲勞失效。
* 疲勞分析
* 可靠度分析
* 有限元素法
### 機械製造
製造類是綜合性科目，需用到固體力學（應用力學（靜力學、動力學）、材料力學）、熱力學、流體力學、熱學、電學、磁學、化學等各方面的理論而實現為成品，此製造程序必需滿足可製造出成品、製造出的成品具有一定水準的精度或強度等要求，且能夠系統化、自動化的生產。此外製造類及實驗類是測量技術使用最多的，自不待言。製造之程序大致有材料之表面處理、熱處理、模具、鑄造、鍛造、焊接、粉末冶金、切削原理、常溫塑性加工、高溫塑性加工、液壓、氣壓、機電整合與自動化製造系統。相關學科：
* 電腦輔助製造
* 機械加工
* 工具機
* 數值控制工具機
* 機械材料
* 量測技術應用
* 鑄造學
* 鍛造學
* 塑膠加工
* 銲接學
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機械工程 | 設計大抵是一綜合性應用的科目，必需作固體力學、熱力學與流體力學之相關計算，必需選取適當的材料，必需設計控制系統，必需為製造之便捷與經濟性作考慮，必需知道市場現況與需求心理學，還要作所有可能的使用安全與更加人性化的考慮，使命重大，正因為它是意想成現實的中間角色。這就是必修課程多的主要原因，一個『人』通常無法都精通這些，所以更突出科技整合的重要性。相關學科：
* 機件原理
* 機構學
* 機械力學
* 機械材料
* 機械製圖
* 波動力學
* 逆向工程
### 固體力學
**固力**旨在探討固體（剛體、彈性體、塑性體）受力引起之平衡、移動與轉動運動、振動、應力、應變、磨擦、塑性流與破壞等，分別有對應的課程，如：靜力學、動力學、材料力學、彈性力學、塑性力學、損傷力學（破壞力學）、斷裂力學、接觸力學、潤滑理論、腐蝕學等。固力的分析同時也是任何設計的基本考慮，設計機械必定是開始於固力中的平衡考慮，依序至振動、強度等考慮，有時還需要周密的考慮，如：疲勞、衝擊、高溫潛變強度等。接著若是流體機械則再作流體力學之計算，然後其能量來源若是熱機，則加入熱力學之計算以提高效率，若是用電能則以電機作計算，再接著則是控制系統之設計，而完成設計工作，再接著才是機械製造、工業工程學、商業管理、商業經濟學等。由這個序列可看出固力大致居機械工程之上游地位。相關學科：
* 靜力學，研究物體於不移動情形下承受已知負載的學問。
* 動力學，研究力如何影響運動中物體的學問。
* 材料力學，研究不同材料在承受不同種類的應力時如何變形的學問。
* 彈性力學、線性彈力
* 塑性力學
* 損傷力學（破壞力學）
* 接觸力學
### 流體力學
流體力學在於討論各種性質的流體及各種流場中，壓力、浮力、阻力、昇力、速度、加速度、能量、波動等問題，並廣泛地應用在水利、土木建築、航空、航海、液壓、氣壓、化工程序等各種工程上。研究流體如何反應出力的學問。流體力學可以被更進一步分成流體靜力學與流體動力學，並且它是連體力學底下的分支。相關學科：
* 空氣靜力學（氣體）
* 空氣動力學（氣體）
* 空氣力學（氣體）
* 水靜力學（液體）
* 水動力學（液體）
* 水力學（液體）
* 液壓（液體）、氣壓（氣體）
* 計算流體力學
* 流體機械
* 紊流理論
* 二相流
#### 應用
* 車輛（空氣）
* 飛機（空氣）
* 船舶（空氣、水）
* 風力發電（空氣）
* 水力發電（水）
### 熱力學與熱科學 | [
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機械工程 | 熱學類課程在於討論熱與能的傳播、利用及對他種物系（物理系或化學系）之影響。相關學科：
* 熱力學
* 熱傳學
* 熱傳遞
* 熱傳導
* 熱對流
* 熱處理
* 熱機學
* 熱流學
* 燃燒學
* 熱流測量技術
* 節能技術
### 電機電子與控制
整合機械工程的力學與電機工程的電力、電子與電路達成所謂機電整合，例如：馬達設計極為標準的機電整合裝置。再者透過控制理論與程式設計的輔助達成整體自動化。相關學科：
* 機電整合
* 自動控制：包含線性控制與非線性控制
* 順序控制
* 微處理機
* 電機學
* 電力學
* 電子學
* 電路學
* 程式設計
* 隨機估測與控制
* 數位邏輯設計
* 系統識別
#### 應用
* 機電整合裝置：馬達
* 光機電整合裝置，如：光碟機
* 機器人學
* 半導體製程控制
## 前瞻研究領域
### 微機電系統
微機電系統是微米大小的機械系統，其中也包括不同形狀的三維平板印刷產生的系統。這些系統的大小一般在微米到毫米之間。在這個大小範圍中日常的物理經驗往往不適用。比如由於微機電系統的面積對體積比要比一般日常生活中的機械系統要大得多，其表面現象如靜電、潤濕等比體積現象如：慣性或熱容量等要重要。他們一般是由類似於生產半導體的技術如表面微加工、體型微加工等技術製造的。其中包括更改的矽加工方法如壓延、電鍍、濕蝕刻、乾蝕刻、電火花加工等等。
生產微機電系統的公司的大小各不相同。大的公司主要集中於為車輛、生物醫療或電子工業生產大批量的便宜的系統。成功的小公司則集中於生產創新的技術。所有這些公司都致力於研究開發。隨著傳感器的發展微機電系統的複雜性和效率不斷提高。
### 奈米技術
奈米科技是一門新興應用科學，其目的在於研究於奈米規模時，物質和設備的設計方法、組成、特性以及應用。奈米科技是許多如生物、物理、化學等科學領域在技術上的次級分類，美國的國家奈米科技啟動計劃將其定義為「1 奈米至 100 奈米尺寸尤其是現存科技在奈米規模時的延伸」。奈米科技的世界為原子、分子、高分子、量子點和高分子集合，並且被表面效應所掌控，如范德瓦耳斯力、氫鍵、電荷、離子鍵、共價鍵、疏水性、親水性和量子穿隧效應等，而慣性和湍流等巨觀效應則小得可以被忽略掉。舉個例子，當表面積對體積的比例劇烈地增大時，開起了如催化學等以表面為主的科學新的可能性。 | [
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機械工程 | 微小性的持續探究以使得新的工具誕生，如：原子力顯微鏡和掃描隧道顯微鏡等。結合如電子束微影之類的精確程序，這些設備將使我們可以精密地運作並生成奈米結構。奈米材質，不論是由上至下製成（將塊材縮至奈米尺度，主要方法是從塊材開始通過切割、蝕刻、研磨等辦法得到盡可能小的形狀（比如超精度加工，難度在於得到的微小結構必須精確）。或由下至上製成（由一顆顆原子或分子來組成較大的結構，主要辦法有化學合成、自組裝和定點組裝。難度在於宏觀上要達到高效穩定的質量，都不只是進一步的微小化而已。物體內電子的能量量子化也開始對材質的性質有影響，稱為量子尺度效應，描述物質內電子在尺度劇減後的物理性質。這一效應不是因為尺度由巨觀變成微觀而產生的，但它確實在奈米尺度時佔了很重要的地位。物質在奈米尺度時，會和它們在巨觀時有很大的不同，例如：不透明的物質會變成透明的（銅）、惰性的物質變成可以當催化劑（鉑）、穩定的物質變得易燃（鋁）、固體在室溫下變成了液體（金）、絕緣體變成了導體（矽）。
奈米科技的神奇來自於其在奈米尺度下所擁有的量子和表面現象，並因此可能可以有許多重要的應用和製造許多有趣的材質。
## 未來展望
能源方面，在近期改進核分裂動力裝置、發展太陽能、地熱、潮汐能、海水溫差能等，可以減少對非再生的化石能源的依賴。從長遠的觀點看，核融合是很有希望的和幾乎無窮盡的未來能源。以核物理學的現在和將來的成就為基礎，機械工程與其他工程技術一起，在 21 世紀中完成核融合動力裝置的開發和推廣可能徹底解決世界的能源問題。使用這種新能源可同時消除對大氣的二氧化碳污染。
地殼中和海水中的金屬礦藏的蘊藏量極為豐富。只要改進採礦和選礦的工藝和提高採、選礦機械的性能，以降低可以經濟利用的礦石品位，並充分回收金屬廢料，在有足夠的能量供應的條件下，金屬材料資源不愁匱乏。
在煤、石油、天然氣等不再被大量地用作燃料而主要作為合成材料的原料之後，非金屬材料的供應也可得到長遠的保證。
化學工程、冶金工程等生產流程中所產生的廢氣、廢水等環境污染源，通過改進流程、增加淨化機械和設施並提高其淨化效率，在技術上是能夠加以消除的。
機械工程一向以增加生產、提高勞動生產率、提高生產的經濟性，即以提高人類的近期利益為目標來研製和發展新的機械產品。在未來的時代，新產品的研製將以降低資源消耗，發展潔淨的再生能源，治理、減輕以至消除環境污染作為超經濟的目標任務。
### 機械工程與人工智慧 | [
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機械工程 | 機械工程是傳統的工程技術。機械可以完成人用雙手和雙目以及雙足雙耳直接完成和不能直接完成的工作，而且完成得更快、更好。現代機械工程創造出越來越精巧和越來越複雜的機械，使過去的許多幻想成為現實。人類現在已能上遊天空和宇宙，下潛大洋深層，遠窺百億光年，近察細胞和分子。新興的電子計算機硬體、軟體科學使人類開始有了加強並部分代替人腦的科技手段，這就是人工智慧。這一新的發展已經顯示出巨大的影響，而在未來年代它還將不斷地創造出人們無法想像的奇蹟。
人類智慧的增長並不減少雙手的作用，相反地卻要求手作更多、更精巧、更複雜的工作，從而更促進手的功能。手的實踐反過來又促進人腦的智慧。在人類的整個進化過程中，以及在每個人的成長過程中，腦與手是互相促進和平行進化的。人工智慧與機械工程之間的關係近似於腦與手之間的關係。其區別僅在於人工智慧的硬體還需要利用機械製造出來。過去，各種機械離不開人的操作和控制，其反應速度和操作精度受到進化很慢的人腦和神經系統的限制。人工智慧消除了這個限制。機械工程可以充分利用這個新出現的巨大可能性。計算機科學與機械工程之間的互相促進，平行前進，將使機械工程在更高的層次上開始新的一輪大發展。
## 參見
* 簡單機械
* 著名機械工程師列表
* 發明家列表
* 專利
* 精密機械
## 參考文獻
### Wikibooks
* Engineering Thermodynamics
* Solid Mechanics
### 相關期刊
* _Experimental Heat Transfer [1] （頁面存檔備份，存於網際網路檔案館）_
* _Heat Transfer Engineering [2] （頁面存檔備份，存於網際網路檔案館）_
* _International Journal for Computational Methods in Engineering Science and Mechanics [3] （頁面存檔備份，存於網際網路檔案館）_
* _International Journal of Optomechatronics [4] （頁面存檔備份，存於網際網路檔案館）_
* _Machining Science and Technology [5] （頁面存檔備份，存於網際網路檔案館）_
* _Materials and Manufacturing Processes [6] （頁面存檔備份，存於網際網路檔案館）_ | [
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] |
機械工程 | * _Mechanics Based Design of Structures and Machines [7] （頁面存檔備份，存於網際網路檔案館）_
* _Mechanics of Advanced Materials and Structures [8] （頁面存檔備份，存於網際網路檔案館）_
* _Nanoscale and Microscale Thermophysical Engineering [9] （頁面存檔備份，存於網際網路檔案館）_
* _Numerical Heat Transfer, Part A [10] （頁面存檔備份，存於網際網路檔案館）_
* _Numerical Heat Transfer, Part B [11] （頁面存檔備份，存於網際網路檔案館）_
* _Tribology Transactions [12] （頁面存檔備份，存於網際網路檔案館）_
### 專業團體
* 香港工程師學會（Hong Kong Institute of Engineering, HKIE）
* 美國機械工程師學會（American Society of Mechanical Engineers）
* Pi Tau Sigma(Mechanical Engineering Honor Society)
* 中國機械工程學會（Chinese Mechanical Engineering Society）
* 英國機械工程師學會（The Institution of Mechanical Engineers）
* 馬來西亞工程師協會（The Institution of Engineers, Malaysia, IEM）
### 延伸閱讀
* Burstall, Aubrey F. A History of Mechanical Engineering. The MIT Press. 1965. ISBN 978-0-262-52001-0.
## 外部連結
* 中國大百科智慧藏
* 英國機械工程師學會官方網站 （頁面存檔備份，存於網際網路檔案館）
* 美國機械工程師學會官方網站 （頁面存檔備份，存於網際網路檔案館）
* 中華民國機械工程學會官方網站 （頁面存檔備份，存於網際網路檔案館） | [
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類光 | 在物理學中，**時空**（英語：spacetime）是一數學模型，其將空間的三個維度和時間的一個維度合併成一個四維流形。時空圖則用來可視化相對論效應，例如為什麼不同的觀察者對事件於何處與何時發生有不同的感知。時空是一種基本概念，分別屬於物理學、天文學、空間物理學和哲學。並且也是這幾個學科最重要的最基本的概念之一。
空間在力學和物理學上，是描述物體以及其運動的位置、形狀和方向等抽象概念；而時間則是描述運動之持續性，事件發生之順序等。時空的特性，主要就是通過物體，其運動以及與其他物體的交互作用之間的各種關係之匯總。
## 概要
時間和空間是人類文明最為古老的概念之一。可追溯至遠古時期，人類的耕作、放牧等日常勞動都需要測量土地、順天時，這就產生了最基礎的時空概念以及度量方法。古代就有「上下四方謂之宇，往古來今謂之宙」的說法。這裡的「宇宙」也就是時空的理念。這也就是誕生了最原始的一維時間和三維空間，並發展同宇宙產生聯繫。
近代科學，無處不涉及時空的概念和測量方法，特別是文藝復興以來，古典力學、物理學和天文學在對時空的認知上基本可以分為兩條不同但相交的線索：
: 其一，以牛頓和馬克士威的重要理論 —— 古典力學和古典電磁學為代表的時間 - 空間概念，經歷愛因斯坦的狹義、廣義相對論，再到現代宇宙論。
: 其二，從牛頓力學經過量子理論、量子力學以及量子場理論，再到量子引力、超弦或 M 理論。
但物理學對於時空的認識還存在不少基本問題尚待解決，還需要進一步完善和發展。
## 理論
### 牛頓的絕對時空概念
#### 絕對時空
利用歐幾里得幾何，測量出長方體的長、寬和高，便能算出其體積。也即是選擇一個可以忽略大小的靜止的參照物，只要得知需要計算物體與其的上下、左右和前後距離，就可以利用歐幾里得幾何計算出。
在描述運動上，需要得知瞬時的速度、加速度和所處位置，這就抽象出一維時間和三維空間的坐標系概念。所以要描述物體的運動，就需要選擇一個可供參考的坐標系，為此，艾薩克・牛頓就創造出四維絕對時空的概念，絕對時間均勻流逝，絕對空間符合三維歐幾里得幾何。絕對時空的本性與任何具體物體以及運動狀態無關。選擇相對於絕對空間的靜止或勻速直線運動為參照所得出坐標，就是慣性參考系。
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類光 | 在古典力學中，任意一個物體對於不同的慣性坐標系的空間坐純量和時間坐純量之間滿足伽利略變換。在此之下，物體的位置和速度都是相對的；而空間位移，時間間隔以及加速度卻是絕對不變的。因為絕對時間的同時性不變，所以相對於同一個慣性參照系的兩個事件同時發生與否也是不變的。而兩個同時發生的事件在其他慣性參照系下也是同時的，這就是絕對同時性。牛頓力學的所有規律（包括萬有引力定律）在內，在伽利略變換下也都是不變的，這即是伽利略相對性原理。
同時，不變性與守恆定律也有著很高相關度。運動狀態在伽利略變換下的時間平移不變性就對應了物體的能量守恆；而空間平移不變性也就與動量守恆相關聯，以及空間轉動不變性更對應了角動量守恆。上述的不變性，就使得絕對時空概念受到了質疑。
這是顯而易見的，因為物體在絕對空間中的運動是可以觀測的，這就有力學運動定律中需要有絕對速度這個概念，但牛頓力學中卻沒有絕對速度一說。即，牛頓力學定律的正確性並不要求存在絕對空間。
雖然不斷有人對牛頓的絕對空間概念提出異議，並且實際上也沒有存在絕對時空的證據。但是牛頓力學和萬有引力等規律是這樣的成功，以至於牛頓的絕對時空的理念，也一直主導著當時的自然科學和哲學界。
#### 致命的問題
牛頓體系推廣到宇宙中則具有局限性。它無法描述一個簡單的宇宙圖像。可以近似描述的宇宙圖像是：在無窮長和無限大的絕對時空中，無數多的星體大致上是靜止的，而且平均光度也是均勻的。然而萬有引力卻讓這個宇宙極為不穩定，甚至無法解答夜晚的天空為什麼是黑的。
#### 馬克士威方程組
19 世紀的物理學有一個重大成就，那就是詹姆斯・克拉克・馬克士威總結前人的電磁學理論，得出來的馬克士威方程組，這裡面出現了光速 c，而後又發現電磁波。
但是依舊受到牛頓的絕對時空概念所支配的物理學家們，自然也認為存在光以太這種物質。所以，馬克士威方程組僅僅只是在絕對空間的慣性參考系中成立，與此類似，電磁波也只是光以太的波動現象而已。
### 愛因斯坦的相對時空觀念
#### 狹義相對論
就在物理學家認為物理的「大廈」即將完工時，兩朵「烏雲」卻讓整個物理體系動搖，更讓人類對時空的認識發生了巨大的改變。
阿爾伯特・愛因斯坦在 1905 年提出的狹義相對論，拓展了伽利略相對性原理，使得包括力學和電磁學在內的所有物理定律在不同慣性參照系也要具有相同的形式。 | [
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類光 | 但是當時的愛因斯坦還假定慣性參考系中單程光速 C 是不變的。據此，不同慣性系的時間 - 空間坐標之間不再遵從伽利略變換，而是遵從勞侖茲變換。
據此，時間間隔（鐘的走動）和空間長度（尺子的長）都成變化的，而且相對於「靜止的」而言，越是高速運動，時鐘就越是變慢，尺子就越是變短。至此，絕對的同時性不存在，也就是說，在一個參照系中同時發生的兩個事件，在另一個高速運動的參照系就不再是同時發生了。
狹義相對論中，因為光速是定量，所以時間 - 空間間隔（時空間隔）就成了不變量。因此，一些慣性系之間，除了對應於時間和空間平移的不變性之能量和動量守恆以外，還存在時空平移不變性。理所當然的，根據能量和動量守恆定律，愛因斯坦推導出他的質量 - 能量關係式（即是眾所周知的 $E=mc^{2}$ ）。這個是原子物理中最為基本的。
#### 閔考斯基時空
狹義相對論不僅判定光以太不存在，它確定電磁波是一種波動，就得出場是一種與「實實在在」的物體不一樣的物質。也判定牛頓的絕對時空不存在，並將一維時間和三維空間聯繫在一起，組成四維時空。赫爾曼・閔考斯基最先發現這一點，即閔考斯基時空。而由此所產生的幾何也成為具有度規張量的歐幾里得幾何，其符合勞侖茲協變性，也就是閔考斯基度規。
#### 廣義相對論
但狹義相對論也有一個缺陷，它無法讓引力定律滿足任何參照系都具有同樣形式。就此，愛因斯坦提出廣義相對論。
依據廣義相對論，在宇宙中就不存在大範圍的慣性參照系，而是只在任意時空點存在局部的慣性系，而不同的慣性系之間就通過慣性力或引力讓其相互聯繫。
就此，慣性力的時空仍然是平直的四維閔克夫斯基時空，反之，引力的時空就是彎曲的四維時空。要描述這樣的四維時空，只能用黎曼幾何來描述。而要想得知時空的彎曲程度，需要知道物質及其能量 - 動量張量，再通過愛因斯坦引力場方程式來確定。
此時，時空不再是物質（物體或者場）的「運動場」，彎曲的時空就是引力場，其性質與在其中運動的物質之性質存在關聯；而時間與空間是物質的存在形式，既沒有脫離物質的時空，也沒有脫離時空的物質。
所以，其一，物質的運動所產生的能量 - 動量作為引力場的源頭，通過場方程式確定引力場的強度，即時空的彎曲度；其二，彎曲時空的幾何特性也同樣決定著物質運動的性質。 | [
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類光 | 例如在太陽系中，太陽作為這個引力場的源頭，它的質量使得整個太陽系的時空發生彎曲。而越靠近太陽，其運動性質受到影響就越大。所以，水星的運動軌跡就受到太陽的影響。而其他恆星所發出的光線在經過太陽邊緣時也發生了偏轉等。實際觀測也證明了廣義相對論的正確。
但廣義相對論也存在著挑戰，20 世紀中期的研究表明，就是在特定的條件下，廣義相對論會讓時空出現「奇異點」。在奇異點處會讓引力場失去意義。
### 宇宙之演化中的整體性
人類對時空認識一直都與宇宙密切相關，而宇宙學原理和愛因斯坦引力場方程式就是現代認識宇宙的基礎。宇宙學原理認定宇宙是一個整體的，它在時間上是不斷變化的，即時間箭頭，而在空間上卻是均勻的。
20 世紀中期，宇宙大爆炸的模型成功的解釋了河外星系紅移，也解釋了夜晚的天空是黑色的，這就是宇宙微波背景輻射。計算預測出的宇宙的演化、星系的形成、輕元素的豐度等在天文觀測上也是大體一致的。便解決牛頓體系沒有給出宇宙圖像的問題。
雖然認識到宇宙是在演化中的一個整體，但是，那個奇異點卻處在宇宙大爆炸的起始、星系或黑洞的中心。
### 量子理論對時空的影響
#### 量子理論
物理學從牛頓的古典力學到 20 世紀初的量子理論，對人類認識時空也起著劇烈的變化，更引發物理學的震盪。
量子力學描述了這樣一個事實，也就是系統的空間位置與動量無法同時精確測量，同樣的，時間與能量之間也是如此。他們滿足不確定性原理；古典軌道在此刻也不再有精確的意義，如何理解量子力學以及有關測量的實質，一直處於爭論中。但在 20 世紀末，有關量子的幾個重要發現更是引發新的疑慮，這就是量子纏結、量子隱形傳態、量子資訊等，在對其研究表明了時空亦有因果性和定域性。
#### 真空
量子力學與狹義相對論結合產生出量子電動力學、量子場論以及電弱統一模型、強作用下的量子色動力學等標準模型。即使巨大的成功也無法掩蓋其中所隱含的原則問題。比如真空與否，存在著零點能以及真空漲落等，讓人們對什麼是真正的「真空」產生了新的認識。
以上述為基礎的產生以下幾個憂慮：量子電動力學的微擾論計算可給出與實驗精密符合的結果，然而這個微擾展開卻是不合理的。
對稱性破缺的機制使傳遞弱作用的中間玻色子獲得質量，然而黑格斯場的真空期望值和前面提到的零點能（相當於宇宙常數），其數值卻比實際觀測到的宇宙常數更大，而且還是驚人的，上百個數量級。 | [
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類光 | 而量子色動力學描述夸克和膠子之間的交互作用，但是被禁閉在強子內的夸克和膠子如何才能獲得自由，這個問題卻是物理學的疑點。
再者，量子論預言到，在 $10^{-33}$ 厘米和 $10^{-43}$ 秒這樣小的時空尺度上，時空的古典概念將不再適用。為解決這個難題，就須要在理論上建立自洽的量子引力理論，即是量子時空理論。然而，量子理論和廣義相對論如何結合一直沒有解決。
一個可能的解決方法就是超弦理論或 M 理論。然而，這個理論卻只有在一維時間 - 九維空間或一維時間 - 十維空間上實現。
這裡又出現了問題，尖銳的矛盾，如何將高維時空應用在低維時空上，也就是人類所熟知的四維時空觀。人們所認知的時空是四維的，也就是說「宇宙」或許就是高維時空中的「一個泡沫」（通常稱為「膜」）。
從高維時空回到四維時空顯然有很多種方法。那麼，在「膜」宇宙以外，是否可能存在其他的「膜」宇宙？在產生宇宙大爆炸之前，是否還會有其他的階段等。這些問題，或許與暗物質、暗能量，以及宇宙常數等問題都有著密切的聯繫。
### 弱作用左右對稱性等的破壞
力學與電磁學規律把慣性系從左手系變為右手系是不會變的，同樣時間反轉亦是不變的。這就是說把時空反演不變的規律與時空本身存在密切關聯。
同時，還存在與這些對稱性相聯繫的正反電荷對稱性。但是在微觀狀態下，在弱作用當中，時空反演不變與正反電荷反演不變這類規律不成立。這就是 20 世紀中期李政道和楊振寧提出宇稱不守恆。這也得到實驗的驗證，不過其中更為深刻的本質尚待物理學家研究。
### 暗能量和宇宙常數
20 世紀末，天文學的重大進展，特別是太空觀測的拓展，讓更多「隱藏」的物體都顯露出來。經過測算基本確定，人類目前還看不見的暗物質占據宇宙總物質 20% 以上，與此類似，與通常的能量完全不同的暗能量占據宇宙中總能量 70%，且宇宙常數為正，約為 $10^{-52}$ $cm^{-2}$ 。
這樣的宇宙時空就不會是平坦的，而是呈現出正的常曲率時空。但這個正的常曲率時空，不僅僅在超弦理論或 M 理論上有著原則性的差別，就連通常意義的量子場論、量子力學，更甚至連古典力學也都出現了疑難。這是因為在理論上沒有一個可公認的方法自洽地定義物理上的可觀測量。而且宇宙常數為什麼這樣小，也是一大難題。
## 參見
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分子 | **分子**（molecule）是一種構成物質的粒子，呈電中性、由單粒或多粒原子組成，原子之間因化學鍵而鍵結。能夠單獨存在、保持物質的化學性質；由分子組成的物質叫**分子化合物**。
一粒分子是由多粒原子在共價鍵中通過共用電子連接一起而形成。它可以由相同的化學元素構成，如氧氣分子 ${\ce {O2}}$ ；也可以由不同的元素構成，如水分子 ${\ce {H2O}}$ 。若原子之間由非共價鍵的化學鍵（如離子鍵）所結合，一般不會視為是單一分子。
在不同的領域中，分子的定義也會有一點差異：在熱力學中，構成物質的分子（如水分子）、原子（如碳原子）、離子（如氯離子）等在熱力學上的表現性質都是一樣的，因此，都統稱為分子；在氣體動力論中，分子是指任何構成氣體的粒子，此定義下，單原子的惰性氣體也可視為是分子。而在量子物理、有機化學及生物化學中，多原子的離子（如硫酸根）也可以視為是一粒分子。
分子可根據其構成原子的數量（原子數）分為單原子分子，雙原子分子等。
在氣體中，氫分子（ ${\ce {H2}}$ ）、氮分子（ ${\ce {N2}}$ ）、氧分子（ ${\ce {O2}}$ ）、氟分子（ ${\ce {F2}}$ ）和氯分子（ ${\ce {Cl2}}$ ）的原子數是 2；固體元素中，黃磷（ ${\ce {P4}}$ ）原子數是 4，硫（ ${\ce {S8}}$ ）的是 8。所以，氬（ ${\ce {Ar}}$ ）是單原子的分子，氧氣（ ${\ce {O2}}$ ）是雙原子的，臭氧（ ${\ce {O3}}$ ）則是三原子的。
許多常見的有機物質都是由分子所組成的，海洋和大氣中大部份也是由分子組成的。但地球上主要的固體物質，包括地函、地殼及地核中雖也是由化學鍵鍵結，但不是由分子所構成。在離子晶體（像食鹽）及共價晶體有反覆出現的晶體結構，但也無法找到分子。固態金屬是用金屬鍵鍵結，也有其晶體結構，但也不是由分子組成。玻璃中的原子之間依化學鍵鍵結，但是既沒有分子的存在，其中也沒有類似晶體反覆出現的晶體結構。
## 歷史
分子的概念最早是由義大利的阿莫迪歐・亞佛加厥提出，他於 1811 年發表了分子學說 ，認為：「原子是參加化學反應的最小質點，分子則是在游離狀態下單質或化合物能夠獨立存在的最小質點。分子是由原子組成的，單質分子由相同元素的原子組成，化合物分子由不同元素的原子組成。在化學變化中，不同物質的分子中各種原子進行重新結合。」 | [
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分子 | 在亞佛加厥之前，化學家約翰・道耳頓在 1803 年及 1811 年提出的定比定律及倍比定律，也支持分子學說，因此許多化學家接受分子學說。可是許多邏輯實證主義者及像恩斯特・馬赫、路德維希・波茲曼、詹姆斯・馬克士威、約西亞・吉布斯等物理學家不接受分子學說，認為分子只是一種方便處理的數學結構，不是實際存在的物質。一直到讓・佩蘭在布朗運動相關的研究中，才證實了分子學說。
## 特性
### 分子大小
大部分的分子無法藉由電子顯微鏡看見，最小的分子是 H2，其鍵長為 0.74 Å。有機合成中常用到的分子大小約從數 Å 至數十 Å。曾經製造過直徑 1000 Å（100 nm）中孔洞氧化矽，是最大的分子。
一般分子雖無法由電子顯微鏡看見，但利用在特定環境下可以用原子力顯微鏡觀察，甚至可以觀察到一些小分子及一些原子的外觀，而像 DNA 是高分子化合物，就可以用電子顯微鏡看見。
大型的分子包括有高分子或超分子等。
#### 半徑
等效分子半徑是指分子在溶液中所佔的大小。
### 分子式
分子的一個特徵就是組成化合物的元素比例總是整數。例如，純水中氫和氧的比例總是 2:1，乙醇中碳、氫、和氧總是以 2:6:1 的比例組合。利用各種元素的比例和化學符號就可以組成分子的實驗式。但是單憑實驗式是無法決定分子的類別 —— 如乙烯的實驗式就與丙烯一樣（同是 CH2），儘管這兩粒分子的原子數或質量都不同。
要反映分子中各種原子的真實數量，就要利用化學式。例如乙烯和丙烯的化學式分別為 ${\ce {C2H4}}$ 和 ${\ce {C3H6}}$ 。
分子量可以用化學式計算而得，是分子質量與 12C 質量的 1/12 之比值。若是網狀固體，則會用化學計量方式計算．稱為式量。
### 分子幾何
由量子力學定律的演算，分子有固定的平衡幾何狀態 —— 鍵的長度和之間的角度。純物質都是由相同幾何結構的分子組合而成的。分子的化學式和結構是決定它的特質，尤其是它的化學活性的兩要素。
同分異構物是指二種化合物組成分子的種類及粒數相同，但其結構不同。同分異構物有相同化學式，但不同結構，不同特質，例如乙醇和甲醚結構不同，但化學式都是 ${\ce {C2H6O}}$ ，屬於結構異構。
立體異構物是一種特別的異構物，它們可以有很相似的物理及化學性質，而由於原子在空間中的排列不同，具有相當不同的生物化學性質，例如維生素 C 有兩種立體異構物，但人體只能吸收其中一種的維生素 C。 | [
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分子 | ### 分子的電氣及光學特性
分子在電場中的特性和分子的電子分佈特性有關，包括其偶極矩及極化性。
分子的電偶極矩是指分子中正電荷和負電荷分佈的不對稱。分子若有對稱中心，例如 ${\ce {H2}}$ ，則偶極矩為零，反之亦然。
分子的極化性是指分子因外在電場作用而改變其電子雲形狀的程度，結果會使得分子會因電場而產生電偶極矩。
分子的光學特性和其在光產生的交流電場下的行為有關，也可以用分子的極化性來得知。極化性和光的折射、散射、光學活性及其他分子光學研究的特性有關。
### 分子的磁特性
大部份化合物的分子及巨分子都是抗磁性。分子的磁化率 $\chi _{m}\,\!$ 是表示外磁場中被磁化的程度，抗磁性性物的磁化率略小於零。
有永久磁矩的分子具有順磁性，包括外層有奇數電子的分子（例如 ${\ce {NO}}$ 及自由基）以及分子中有部份原子的內層電子未填滿（如過渡金屬）。順磁性物質的磁化率會隨溫度而變化，因為電子的熱運動會降低磁場中的磁矩。
## 分子間作用力
分子間作用力是指電中性的分子在空間中的作用力，會隨著分子的極性而不同，其作用力相當複雜，一直到了量子力學出現後才對分子間作用力有進一步的了解。
兩粒極性分子（總偶極矩不為零的分子）之間會有分子間作用力，可能會使分子相吸或是排斥，若分子的偶極矩沒有互相抵消，其作用力會變強。
若是一粒極性分子和一粒非極性分子，會有產生誘導性的分子間作用力。極性分子會極化非極性分子，若極性分子的負電荷較靠近非極性分子，會誘導非極性分子，使其正電荷較靠近極性分子。
分散力是指兩粒非極性分子之間的分子間作用力。一般來說，非極性分子的總偶極矩為零，不過在特定時間，因為電子在分子中的分佈情形，會產生瞬時偶極。瞬時偶極可能會極化其他的非極性分子，或是兩粒有瞬時偶極的分子會互相影響。
## 相關理論
分子物理學及理論化學的研究主要是基於量子力學，對於化學鍵的了解相當重要。最簡單的分子是氫分子離子 ${\ce {{H2}^{+}}}$ ，而化學鍵中最簡單的是單電子鍵。 ${\ce {{H2}^{+}}}$ 由二粒帶正電的質子及一粒帶負電的電子組成，因為沒有電子和電子之間的斥力，薛丁格方程式會相關簡單，易於求解。隨著快速數位電腦的發展，也可以計算一些更複雜分子的近似解，這也是計算化學的一片主要領域。 | [
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分子 | 科學家試著嚴格的定義哪些原子的組合穩定到可以視為是分子的程度，而 UPAC 的建議是「需對應位能面的一片低坑，而且要深到可以限制至少一個振動態。」。此定義和原子之間交互關係的本質無關，和交互關係的強度有關。事實上，這也包括一些弱鍵結，以往不會視為是分子的一些原子團，例如氦二聚體 ${\ce {He2}}$ ，有一個振動束縛態，其鍵結非常鬆散，可能只能在非常低溫時才可以觀測到。
原子的組合是否夠穩定到可視為分子，在本質上是操作性的定義。在哲學上，分子不是基本實體（相反，基本粒子就是基本實體），分子的概念可以視為是化學家在陳述世界上原子之間作用力強度的一種敘述方式。
### 分子光譜學
分子光譜學是處理分子和帶有已知能量（依照普朗克關係式，也可以表示為頻率）的探測信號（或粒子）作用時，產生的頻譜。可以由分子吸收光譜或發射光譜來分析其能量交換，進而分析分子的量子化能階。當像中子或電子等粒子或是高能的 X 光和一般規則排列的分子（如晶體）作用時，光譜學的研究一般不會指其繞射的現象。
分子的電磁及光學特性都和分子在不同狀態下的波函數及能量有關。分子光譜可以得到分子的狀態，以及在各狀態之間躍遷的機率。
分子光譜依原子的質量，位置以及原子間的交互作用有關。分子光譜和分子的轉動慣量有關，利用分子光譜，可以準確的得到原子間作用力的數值。分子光譜中線段和頻帶的數量和其分子的對稱性有關。
分子電子躍遷和分子中電子雲的結構及化學鍵的狀態有關。若分子光譜中有吸收許多在長波長可見光範圍的能量，分子會有顏色，像很多有機染料都屬於這一類。
## 化學、物理學及生物學中的分子
分子是化學的基礎概念，大部份有有關分子結構及功能的資訊都要透過化學研究才能得到。分子結構決定了化學反應的特性。
分子的結構及性質都是被分子物理學中研究的物理現象所影響。在物理上，分子的概念可以說明氣體、液體及固體的特性。例如分子擴散的能力、黏度、導熱係數等。第一次直接證明分子存在的實驗是在 1906 年由法國科學家讓・佩蘭，在研究布朗運動時發現的。
所有生物都是因為分子間的化學、非化學作用巧妙平衡而存活。對於分子結構及特性的研究是在生物學或是科學上都很重要。
生物學、化學及分子物理學的進展產生了分子生物學，依照生物中基本化合物的結構及特性，研究生物的基本特性。
## 相關條目
## 參考文獻
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蛋白质 | **蛋白質**（英語：protein）舊稱「**朊**」，常簡稱「蛋白」，是大型生物分子，或高分子，它由一個或多個由 α- 胺基酸殘基組成的長鏈條組成。α- 胺基酸分子呈線性排列，相鄰 α- 胺基酸殘基的羧基和胺基通過肽鍵連接在一起，最後經過折疊形成有功能的立體結構。蛋白質的 α- 胺基酸序列是由對應基因所編碼。除了遺傳密碼所編碼的 20 種「標準」胺基酸，在蛋白質中，某些 α- 胺基酸殘基還可以被改變原子的排序而發生化學結構的變化，從而對蛋白質進行活化或調控。多個蛋白質和礦物質可以一起，往往是通過結合在一起形成穩定的蛋白質錯合物，這樣的大分子結構就像機械一樣，來發揮某一特定功能。
與其他生物大分子（如多醣和核酸）一樣，蛋白質是地球上生物體中的必要組成成分，參與了細胞生命活動的每一個進程。蛋白酶是最常見的一類蛋白質，它們催化生物化學反應，尤其對於生物體的代謝至關重要。除了酶之外，還有許多結構性或機械性蛋白質，如肌肉中的肌動蛋白和肌球蛋白，以及細胞骨架中的微管蛋白（參與形成細胞內的支撐網絡以維持細胞外形）。另外一些蛋白質則參與細胞信號傳導、免疫反應、細胞黏附和細胞週期調控等。同時，蛋白質也是動物飲食中必需的營養物質，這是因為動物自身無法合成所有蛋白胺基酸，動物需要和必須從食物中獲取必需胺基酸。通過消化過程將蛋白質降解為自由胺基酸，動物就可以將它們用於自身的代謝。
## 生物化學性質
蛋白質是由不同的 L 型 α 胺基酸所形成的線性聚合物。目前在絕大多數已鑑定的天然蛋白質中發現的胺基酸有 20 種（參見標準蛋白胺基酸列表）。不過在自然界中還存在著一些特殊的胺基酸，例如在一種海洋寡毛綱小蠕蟲 _Olavius algarvensis_ 以及與之存在共生關係的細菌 δ1（該細菌屬於 δ 變形菌）中存在著高含量的硒代半胱胺酸，由原本為終止密碼子的 UGA 編碼，和吡咯賴胺酸，由終止密碼子 UAG 編碼。 | [
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蛋白质 | 所有胺基酸都有共同的結構特徵，包括與胺基連接的 α 碳原子，一個羧基和連接在 α 碳原子上的不同的側鏈。但脯胺酸有著與這種基本結構不同之處：它含有一個側鏈與胺基連接在一起所形成的特殊的環狀結構，使得其胺基在肽鍵中的構象相對固定。 標準胺基酸的側鏈是構成蛋白質結構的重要元素，它們具有不同的化學性質，因此對於蛋白質的功能至關重要。多肽鏈中的胺基酸之間是通過脫水反應所形成的肽鍵來互相連接；一旦形成肽鍵成為蛋白質的一部分，胺基酸就被稱為「殘基」，而連接在鏈的碳、氮、氧原子被稱為「主鏈」或「蛋白質骨架」。由於肽鍵有兩種共振態，具有一定的雙鍵特性，使得相鄰 α 碳之間形成肽平面；而肽鍵兩側的二面角確定了蛋白質骨架的局部形態。
由於胺基酸的非對稱性（兩端分別具有胺基和羧基），蛋白質鏈具有方向性。蛋白質鏈的起始端有自由的胺基，被稱為 N 端或胺基端；尾端則有自由的羧基，被稱為 C 端或羧基端。
「蛋白質」、「多肽」和「肽」這些名詞的含義在一定程度上有重疊，經常容易混淆。「蛋白質」通常指具有完整生物學功能並有穩定結構的分子；而「肽」則通常指一段較短的胺基酸寡聚體，常常沒有穩定的三維結構。然而，「蛋白質」和「肽」之間的界限很模糊，通常以 20-30 個殘基為界。「多肽」可以指任何長度的胺基酸線性單鏈分子，但常常表示缺少穩定的三級結構。
## 合成
### 蛋白質生物合成 | [
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蛋白质 | 每一種蛋白質都有自己獨特的胺基酸序列，而胺基酸序列的組成資訊則由編碼對應蛋白質的基因的核苷酸序列所決定。遺傳密碼是一套由三個核苷酸組成的密碼子，每一種三個核苷酸的組合可以編碼一種特定胺基酸，如 mRNA 上的 AUG（在 DNA 中為 ATG）編碼甲硫胺酸。由於 DNA 含有四種核苷酸（A、T、C、G），所以對應的可能的密碼子有 4×4×4=64 種；而標準胺基酸只有 20 種，因此有部分密碼子是冗餘的，即部分胺基酸可以由多個不同的密碼子所編碼。DNA 中的基因首先在 RNA 聚合酶等蛋白質的作用下被轉錄為前 mRNA。在大多數生物體中，前 mRNA（或初始轉錄產物）要經過轉錄後修飾以形成成熟的 mRNA，隨後 mRNA 就可以經由核糖體被用作蛋白質合成的模板。在原核生物中，mRNA 可能可以在生成後被直接用於蛋白質合成，或者在離開類核後就結合核糖體。而在真核生物中，mRNA 在細胞核中被合成，然後通過核膜被轉運到細胞質中；在細胞質中，mRNA 才可以被用於蛋白質合成。原核生物的蛋白質合成速率可以達到每秒 20 個胺基酸，要高於真核生物。
從一個 mRNA 模板合成一個蛋白質的過程被稱為轉譯。在轉譯過程中，mRNA 被一些蛋白質攜帶到核糖體上；然後核糖體在 mRNA 上從 5' 端到 3' 端尋找起始密碼子（大多數情況下為 AUG）；找到起始密碼子後，即核糖體上起始 tRNA 的反密碼子與起始密碼子配對後，轉譯就可以開始進行；在起始密碼子後，核糖體每一次閱讀三個核苷酸（或一個密碼子），同樣是通過攜帶對應胺基酸的 tRNA 上反密碼子與密碼子配對。其中，胺醯 tRNA 合成酶可以將 tRNA 分子與正確的胺基酸連接到一起。不斷延長的多肽鏈通常被稱為「新生鏈」。生物體中的蛋白質合成總是從 N - 端到 C - 端。
合成的蛋白質的大小可以通過其含有的胺基酸數目或者其分子量（以道爾頓或千道爾頓，即 kDa 為單位）來衡量。酵母蛋白的平均長度為 466 個胺基酸或平均分子量為 53kDa。目前已知的最大蛋白質是肌聯蛋白，它是肌肉中肌節的組分之一，其分子量為近 3,000 kDa，含有近 27,000 個胺基酸。
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蛋白质 | 除了生物合成外，一些小的蛋白質可以通過多種化學途徑來合成。這些合成方法又被稱為肽合成，其依賴於有機合成技術，如化學連接來高通量生產肽。化學合成允許在合成的肽鏈中引入非天然胺基酸，如加入螢光標記的胺基酸。這些合成方法所合成的產物被大量應用於生物化學和細胞生物學實驗。但是，化學合成無法有效合成殘基數多於 300 的蛋白質，而且合成的蛋白質可能不具有天然的三級結構。大多數化學合成方法都是從 C - 端到 N - 端進行合成，剛好和生物合成反應的方向相反。
## 降解
對於細胞來說，蛋白質降解有多種用途，包括去除分泌蛋白的 N 末端信號肽，對前體蛋白進行剪切以產生「成熟」蛋白等。細胞不需要的或受到損傷的非跨膜蛋白質一般由蛋白酶體來進行降解，而真核生物的跨膜蛋白則通過內體運送到溶體（動物細胞）或液胞（酵母）中進行降解。降解所生成的胺基酸分子可以被用於合成新的蛋白質。一些蛋白質可以發生自降解。此外，細胞中存在的大量蛋白酶（特別是溶體中），可以對外來的蛋白質進行降解，這也是一種細胞自我保護的機制。
生物學實驗中，也經常對蛋白質進行降解分析；例如在蛋白質體學中，利用蛋白酶對特定蛋白質進行降解，並對降解產物進行質譜分析而獲得對應蛋白質的序列資訊和修飾情況；此外，生物化學實驗中，埃德曼降解法常被用於對蛋白質進行胺基酸序列分析。
## 結構
大多數的蛋白質都自然摺疊為一個特定的三維結構，這一特定結構被稱為天然狀態。雖然多數蛋白可以通過本身胺基酸序列的性質進行自我摺疊，但還是有許多蛋白質需要分子伴侶的幫助來進行正確的摺疊。在高溫或極端 pH 等條件下，蛋白質會失去其天然結構和活性，這一現象就稱為變性。生物化學家常常用以下四個方面來表示蛋白質的結構：
* 蛋白質一級結構：組成蛋白質多肽鏈的線性胺基酸序列。一個蛋白質是一個聚醯胺。
* 蛋白質二級結構：依靠不同胺基酸之間的 C=O 和 N-H 基團間的氫鍵形成的穩定結構，主要為 α 螺旋和 β 摺疊。因為二級結構是局部的，不同的二級結構的許多區域可存在於相同的蛋白質分子。
* 蛋白質三級結構：通過多個二級結構元素在三維空間的排列所形成的一個蛋白質分子的三維結構，是單個蛋白質分子的整體形狀。蛋白質的三級結構大都有一個疏水核心來穩定結構，同時具有穩定作用的還有鹽橋 (蛋白質)、氫鍵和二硫鍵，甚至轉譯後修飾。「三級結構」常常可以用「摺疊」一詞來表示。三級結構控制蛋白質的基本功能。 | [
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蛋白质 | * 蛋白質四級結構：由幾個蛋白質分子（多肽鏈），通常稱為蛋白質亞基所形成的結構，在功能上作為一個蛋白質複合體。
蛋白質並不完全是剛性分子。許多蛋白質在執行生物學功能時可以在多個相關結構中相互轉換。在進行功能型結構重排時，這些相關的三級或四級結構通常被定義為不同「構象」，而這些結構之間的轉換就被稱為「構象變換」。例如，酶的構象變換常常是由受質結合到活性位點所導致。在溶液中，所有的蛋白質都會發生結構上的動態變化，主要表現為熱振動和與其他分子之間碰撞所導致的運動。
蛋白質可以由三級結構的不同大致分為三個主要類別：球蛋白、纖維蛋白和膜蛋白。幾乎所有的球蛋白都是水溶性的，許多球蛋白是酶。纖維蛋白多為結構性的，例如，結締組織的主要成分膠原蛋白，或頭髮和指甲的蛋白質成分角蛋白。膜蛋白常常作為受體，或提供通道極性的或帶電的分子通過細胞膜。
要了解特定蛋白質的功能，獲得其三級結構或四級結構可以提供重要的結構資訊。目前用於蛋白質的原子解析度結構測定的方法主要是 X 射線晶體學和 NMR 光譜學。冷凍電子顯微學也可以提供超大蛋白質錯合物（如病毒、核糖體等）的低解析度結構資訊。而電子晶體學在一些情況下也可以提供較高解析度的結構資訊，特別是對於膜蛋白的二維晶體。解析的結構（包括原子坐標和結構解析的相關資訊）通常存放到蛋白質資料庫（PDB），供全世界研究者免費下載。蛋白質結構預測也可以為未知結構（實驗結構）的蛋白質提供結構資訊。
## 細胞功能
蛋白質是細胞中的主要功能分子。除了特定類別的 RNA，大多數的其他生物分子都需要蛋白質來調控。蛋白質也是細胞中含量最為豐富的分子之一；例如，蛋白質占大腸桿菌細胞乾重的一半，而其他大分子如 DNA 和 RNA 則只分別占 3% 和 20%。在一個特定細胞或細胞類型中表現的所有蛋白被稱為對應細胞的蛋白質體。
蛋白質能夠在細胞中發揮多種多樣的功能，涵蓋了細胞生命活動的各個方面：發揮催化作用的酶；參與生物體內的新陳代謝的調劑作用，如胰島素；一些蛋白質具有運輸代謝物質的作用，如離子泵和血紅素；可以消耗能量來轉動並運動的分子馬達；控制神經和反應的神經傳遞物；發揮儲存作用，如植物種子中的大量蛋白質，就是用來萌發時的儲備；許多結構蛋白被用於細胞骨架等的形成，如肌球蛋白；還有免疫、細胞分化、細胞凋亡等過程中都有大量蛋白質參與。 | [
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蛋白质 | 蛋白質功能發揮的關鍵在於能夠特異性地並且以不同的親和力與其他各類分子，包括蛋白質分子結合。蛋白質結合其他分子的區域被稱為結合位點，而結合位點常常是從蛋白質分子表面下陷的一個「口袋」；而結合能力與蛋白質的三級結構密切相關，因為結構決定了結合位點的形狀和化學性質（即結合位點周圍的胺基酸殘基的側鏈的化學性質）。蛋白質結合的緊密性和特異性可以非常高；例如，核糖核酸酶抑制蛋白可以與人的血管促生蛋白以亞飛莫耳（sub-femtomolar，即 < 10-15 M）量級的解離常數進行結合，但卻完全不結合（解離常數 > 1 M）angiogenin 在兩棲動物中的同源蛋白抗腫瘤核糖核酸酶。）非常微小的化學結構變化，如在結合位點的某一殘基側鏈上添加一個甲基基團，有時就可以幾乎完全破壞結合；例如，胺醯 tRNA 合成酶可以分辨側鏈結構非常類似的纈胺酸和異白胺酸，而這兩種胺基酸的差別就在於異白胺酸的側鏈多出一個甲基。相同的蛋白質分子結合在一起就可形成同源寡聚體或多聚體，有些多聚體可以形成纖維；而這些形成纖維的蛋白質往往是結構蛋白，它們在單體狀態下是球蛋白，通過自結合來形成剛性的纖維。蛋白 - 蛋白相互作用可以調控酶的活性和細胞週期中的各種進程，並可以使大型的蛋白質錯合物得以形成，這樣可以將參與同一生物學功能的分子結合到一起，從而提高其工作效率；而結合所誘導的蛋白構象變化對於複雜的信號傳導網絡的構建也是必不可少的。還有一些蛋白質（如膜蛋白）可以結合或者插入到細胞膜中。
### 催化作用
細胞中，酶是最被廣泛了解和研究最多的蛋白質，它的特點是催化細胞中的各類化學反應。酶的催化反應具有高度的專一性和極高的催化效率。酶在大多數與代謝和異化作用以及 DNA 的複製、修復和 RNA 合成等相關的反應中發揮作用。在轉譯後修飾作用中，一些酶（如激酶和磷酸酶）可以在其受質蛋白質上增加或去除特定化學基團（如磷酸基團）。目前已知的酶催化的反應有約 4000 種。酶可以極大地加速其所催化的反應；例如，與沒有酶催化的情況相比，乳清酸核苷 - 5'- 單磷酸脫羧酶的加速作用最高可達 1017 倍（形象地說，在沒有酶的情況下完成反應需要七千八百萬年，而存在酶的情況下反應只需 18 毫秒）。 | [
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蛋白质 | 結合於酶上，並在酶的作用下發生反應的分子被稱為受質。雖然酶分子通常含有數百個胺基酸殘基，但參與與受質結合的殘基只占其中的一小部分，而直接參與受質催化反應的殘基則更少（平均為 3-4 個殘基）。這部分參與受質結合和催化的區域被稱為活性位點。有一些酶需要結合一些小分子（輔酶或輔因子）才能夠有效發揮催化作用。酶的活性還可以被酶抑制劑所抑制，或被酶活化劑所提高。
### 訊號傳遞和物質運輸
許多蛋白質都參與了細胞中和細胞間的訊號傳遞。一些蛋白質，如胰島素，作為細胞外蛋白質，可以將訊號從一個細胞（合成這些蛋白質的細胞）傳送到身體其他組織中的細胞。還有一些蛋白質，如屬於膜蛋白的受體，可以結合細胞外的訊號分子來引發細胞內的生物化學反應；多數受體都有一個位於細胞外表面的結合域〔結合訊號分子〕和一個位於細胞內的效應結構域（可能具有酶活性或可以發生構象變化以誘發與細胞內其他蛋白質的結合），兩者之間通過跨膜域連接。
抗體是適應性免疫系統中重要的組成蛋白質，其作用為結合抗原或機體中的其他外來物質，通過識別來引發免疫系統消除這些物質。抗體可以被分泌到細胞外環境中或錨合到特異性 B 細胞（即漿細胞）的細胞膜中。抗體和抗原之間存在很高的親和力，使得抗體可以很快地識別抗原。
在多細胞生物體中，載體運輸蛋白能夠結合特定的小分子並將它們運送到機體中的特定位置。這些蛋白質在運輸的起點（往往具有較高的濃度）必須以高的親和力結合它們的運輸物，而在目的組織中（運輸物質濃度較低）則必須釋放所結合的物質。這就需要運輸蛋白和所結合的物質之間有特定的親和力。一個典型的例子是血紅素，它作用是將氧氣從肺中運輸到其他組織和器官中。
通道蛋白也是重要的物質運輸蛋白，它們能夠改變細胞膜的通透性，使得一些小分子和離子可以進出細胞。膜本身是疏水性的，極性或帶電分子無法通過擴散作用穿過。作為跨膜蛋白的通道蛋白，含有可控制的內部通道，在一定條件下允許這些分子進出細胞。通道蛋白也有專一性，許多離子通道蛋白只選擇性地對特定離子起作用；例如，鉀離子和鈉離子通道分別只識別鉀離子或鈉離子。
### 變性作用
蛋白質受到酸、鹼、尿素、有機溶酶、重金屬、熱、紫外光及 X - 射線等物理或化學的破壞，引起蛋白質自然之分子結構的改變，並引起生理活性的消失。
變性作用破壞了蛋白質的二級、三級、四級結構，一般不會影響其初級結構。
#### 變性蛋白質的特性
1. 溶解度降低。
2. 生物活性消失。
3. 不能結晶。 | [
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蛋白质 | 4. 易受蛋白脢的水解。
5. 滴定曲線改變，因可滴定的官能基增加。
6. -SH 等基團的反應活性增加。
### 結構蛋白
結構蛋白能夠形成相對更為剛性的生物組分。多數結構蛋白為纖維蛋白；膠原蛋白和彈性蛋白是結締組織（如軟骨）中關鍵的組分，而角蛋白則存在於頭髮、指甲、羽毛、蹄和一些貝殼中。此外，肌動蛋白和微管蛋白作為單體是球狀可溶蛋白，但一旦多聚化便形成長的剛性纖維用於組成細胞骨架，以保持細胞的大小和形態。
其他結構蛋白還包括馬達蛋白，如肌球蛋白、運動蛋白和動力蛋白，它們能夠產生動力。這些蛋白質對於細胞能動性（特別是精子的運動）、細胞內物質運輸和細胞分裂都具有重要作用；它們也為肌肉收縮提供動力。
## 研究方法
蛋白質是被研究得最多的一類生物分子，對它們的研究包括「體內」(in vivo)、「體外」(in vitro)、和「在矽之中」(in silico)。體外研究多應用於純化後的蛋白質，將它們置於可控制的環境中，以期獲得它們的功能資訊；例如，酶動力學相關的研究可以揭示酶催化反應的化學機制和與不同受質分子之間的相對親和力。相反的，**體內**研究實驗著重於蛋白質在細胞或者整個生物中的活性作用，從而可以了解蛋白質發揮功能的場所和相應的調節機制。**在矽之中**研究使用的計算方法來研究蛋白質。
### 蛋白質純化
為了進行體外 (in vitro) 研究，必須先將目的蛋白質從其他細胞組分中分離提純出來。這一過程通常從細胞裂解開始（對於分泌性蛋白質的提純則不需要裂解細胞），通過破壞細胞膜將細胞內含物釋放到溶液中，從而獲得含有目的蛋白質的細胞裂解液。然後通過超速離心將細胞裂解液中膜脂和膜蛋白、胞器、核酸以及含有可溶蛋白質的混合物。鹽析法是一種較為常用的通過沉澱從裂解液中分離濃縮蛋白質的方法。基於目的蛋白質的化學性質（如分子量、帶電情況和結合活性），可以利用不同的色譜法來進一步分離提純蛋白質。純化的程度可以用電泳（已知目的蛋白質的分子量）、光譜學（目的蛋白質具有獨特的光譜學特徵）或者酶活分析反應（目的蛋白質具有特定的酶活性）來衡量。另外，蛋白質可以使用電聚焦根據其電荷被分離
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蛋白质 | 對於天然蛋白質，可能需要一系列的純化步驟才能獲得純度足以用於實驗室應用的蛋白質。為了簡化這一過程，通常採用基因工程的手段在目的蛋白質上添加一些化學特性，在不改變其結構和生物學活性的情況下使純化過程更為簡單。通常是將含有特定胺基酸序列的「標籤」連接在目的蛋白質的 N - 端或 C - 端。例如，含有連續多個組胺酸的序列，稱為組胺酸標籤；將含有帶組胺酸標籤蛋白質的裂解液流過含有鎳的親和層析柱，組胺酸就可以與鎳螯合從而結合在柱子上，而裂解液中其他蛋白質由於沒有組胺酸標籤而直接流出柱子，從而達到分離目的。通過基因工程（即 DNA 重組）改造而獲得的蛋白質被稱為重組織蛋白質。
### 細胞內定位
_in vivo_ 的蛋白質研究常常專注於蛋白質在細胞中的合成和定位。雖然已經知道許多細胞內蛋白質是在細胞質中合成，而膜結合蛋白質或分泌性蛋白質是在內質網中合成，但蛋白質定位到特定胞器或細胞結構的特異性是如何達到的，目前還不清楚。一些有助於獲得特定蛋白質在細胞中定位的方法得到了發展，特別是用基因工程將目的蛋白質上連接上「報告者」（如綠色螢光蛋白），將這樣的融合蛋白在細胞中表現後，就可以通過顯微鏡觀察螢光來了解融合蛋白在細胞中的分布。
另一種常用的同樣是基因工程的方法為定點突變。利用這一方法，研究者可以改變蛋白質序列，從而改變其結構、細胞內定位以及調控機制；而這些改變可以在 _in vivo_ 的情況下通過連接綠色螢光蛋白，或者在 _in vitro_ 的情況下通過酶動力學的方法以及結合實驗進行觀察。
### 蛋白質體學
在一定時間內一個細胞或一類細胞中存在的所有蛋白質被稱為蛋白質體，研究如此大規模的資料的領域就被稱為蛋白質體學，與基因組學的命名方式相似。蛋白質體學中關鍵的實驗技術包括用於檢測細胞中大量種類蛋白質相對水平的蛋白質微陣列技術，和用於系統性研究蛋白 - 蛋白相互作用的雙雜交篩選技術。此外，還有探究所有組分之間的可能的生物學相互作用的相互作用組學，以及系統性地解析蛋白質結構，並揭示其中的可能的摺疊類型的結構基因組學。
分析基因組和蛋白質體資料，這就需要應用計算技術於生物學問題，如基因識別和支序分類。生物資訊學領域現在是基因和蛋白質的分析必不可少的。
### 生物資訊學
大量的計算方法已經被開發來分析蛋白質的結構，功能和進化。 | [
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] |
蛋白质 | 這樣的工具的開發是由可用的多種生物體（包括人類基因組）的大量基因組和蛋白質體資料驅動的。根本不可能通過實驗來研究所有的蛋白質，因此只有少數蛋白質被得到實驗室實驗，而計算工具用於外推到相似的蛋白質。
### 結構預測與模擬
作為結構基因組研究的互補，蛋白質結構預測的目標是發展出有效的能夠提供未知結構（未通過實驗方法得到）蛋白質的可信的結構模型。目前最為成功的結構預測方法是同源建模；這一方法是利用序列相似的蛋白質（已知結構）的結構作為「模板」。而結構基因組的目標正是通過解析大量蛋白質的結構來為同源建模提供足夠的模板以獲得剩餘的未解析的同源蛋白結構。從序列相似性較差的模板計算出精確的結構模型對於同源建模法還是一個挑戰，問題在於序列比對準確性的影響，如果能夠獲得「完美」的比對結果，則能夠獲得精確的結構模型。許多結構預測方法已經被用於在蛋白質工程領域，在這些方法的幫助下，研究者們設計出一些新型的蛋白質摺疊類型。更為複雜的結構計算是預測蛋白質分子之間的相互作用，需要應用分子對接法和蛋白 - 蛋白相互作用預測。
利用分子動力學的方法可以模擬蛋白質的摺疊和結合過程。通過分布式計算，如 Folding@Home 計劃，為分子動力學模擬注入了活力。小的 α 螺旋蛋白結構域，如絨毛蛋白的頭部和 HIV 輔助蛋白已經成功地在計算機中（_in silico_）被模擬。將標準的分子動力學和量子力學計算相結合的混合方法已經被用於探索視紫紅質分子的電子態。
## 蛋白質含量檢測
蛋白質含量檢測，通常是檢測樣本裡的含氮量比例。但是，凱氏分析與杜馬斯方法，分辨不出蛋白質與三聚氰胺的差異。一份純瘦肉的雞胸肉以凱氏分析，可以測得數值約 31% 左右。
* 凱氏分析（凱氏定氮法）
* 杜馬斯方法（杜馬斯燃燒定氮法）
* 近紅外光譜法
## 營養作用
大多數微生物和植物能夠合成所有 20 種標準胺基酸；動物則由於缺乏某些胺基酸合成途徑中特定胺基酸合成反應所需的關鍵酶，如從天門冬胺酸生成離胺酸、甲硫胺酸和蘇胺酸的合成反應第一步中發揮催化作用的天門冬胺酸激酶，而只能合成部分胺基酸。因此，動物必須從食物中獲取這些自身無法合成的胺基酸。一個生物體所無法合成而需從食物中獲取的胺基酸被稱為必需胺基酸；而食物中缺少必需胺基酸的蛋白質，被定位為不完全蛋白質。如果環境中存在所需胺基酸，微生物能夠直接攝取這些胺基酸，而下調其自身的合成水平，從而節省了原來需要用於合成反應的能量。 | [
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蛋白质 | 動物所攝取的胺基酸來源於食物中所含的蛋白質，每公克蛋白質可供給 4 大卡熱量。攝入的蛋白質通過消化作用而被降解，這一過程通常包括蛋白質在消化系統的酸性環境下發生變性，變性後的蛋白質被蛋白酶水解成胺基酸或小段的肽。隨後這些降解片段就可以被吸收。部分吸收後的胺基酸被用於蛋白質的合成，其餘的則通過糖質新生作用被轉化為葡萄糖或進入三羧酸循環進行代謝。蛋白質的營養作用在飢餓環境下顯得特別重要，此時機體可以利用自身的蛋白質，特別是肌肉中的蛋白質，來產生能量以維持生命活動。蛋白質 / 胺基酸也是食物中重要的氮源.
蛋白質進入口腔時無法被分解，進而到胃。胃蛋白酶可斷裂芳香族胺基酸或白胺酸胺基端肽鍵，凝乳酶可將牛奶中的酪蛋白（Casein）催化成含鈣的副乾酪素（Ca paracaseinate）。
到了小腸，胰蛋白酶、糜蛋白酶、羧基肽酶開始作用；胰蛋白酶可斷裂離胺酸或精胺酸的羧基端肽鍵，糜蛋白酶可斷裂色胺酸、酪胺酸、苯丙胺酸的羧基端肽鍵，羧基肽酶可斷裂肽鏈羧基端的最後一個肽鍵。
人體所需蛋白質在許多食物中都含量豐富，如動物肌肉、乳製品、蛋、豆類、穀類和蕈類等。人體中蛋白質缺乏可以導致全身浮腫、皮膚乾燥病變、頭髮稀疏脫色、肌肉重量減輕、免疫力下降等。
食物中的蛋白質有時會引起過敏反應。
高蛋白飲食會加重心臟病的狀況，膽固醇問題會使其上升到不健康的水平。
## 歷史和詞源
在 18 世紀，安東尼奧・弗朗索瓦和其他一些研究者發現蛋白質是一類獨特的生物分子，他們發現用酸處理一些分子能夠使其凝結或絮凝。當時他們注意到的例子有來自蛋清、血液、血清白蛋白、纖維素和小麥麵筋裡的蛋白質。荷蘭化學家格哈杜斯・約翰內斯・穆德對一般的蛋白質進行元素分析發現幾乎所有的蛋白質都有相同的實驗式。用「蛋白質」這一名詞來描述這類分子是由穆德的合作者永斯・貝采利烏斯於 1838 年提出。穆德隨後鑑定出蛋白質的降解產物，並發現其中含有為胺基酸的白胺酸，並且得到它（非常接近正確值）的分子量為 131 原子質量單位。
對於早期的生物化學家來說，研究蛋白質的困難在於難以純化大量的蛋白質以用於研究。因此，早期的研究工作集中於能夠容易地純化的蛋白質，如血液、蛋清、各種毒素中的蛋白質以及消化性和代謝酶（獲取自屠宰場）。1950 年代後期，Armour Hot Dog 公司純化了一公斤純的牛胰腺中的核糖核酸酶 A，並免費提供給全世界科學家使用。目前，科學家可以從生物公司購買越來越多的各類純蛋白質。 | [
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蛋白质 | 著名化學家萊納斯・鮑林成功地預測了基於氫鍵的規則蛋白質二級結構，而這一構想最早是由威廉・阿斯特伯里於 1933 年提出。隨後，沃爾特・考茲曼在總結自己對變性的研究成果和之前凱伊・林諾斯特倫・郎的研究工作的基礎上，提出了蛋白質摺疊是由疏水相互作用所介導的。1949 年，弗雷德里克・桑格首次正確地測定了胰島素的胺基酸序列，並驗證了蛋白質是由胺基酸所形成的線性（不具有分叉或其他形式）多聚體。原子解析度的蛋白質結構首先在 1960 年代通過 X 射線晶體學獲得解析；到了 1980 年代，核磁共振也被應用於蛋白質結構的解析；近年來，冷凍電子顯微學被廣泛用於對於超大分子複合體的結構進行解析。
蛋白質這一概念最早是由瑞典化學家永斯・貝采利烏斯於 1838 年提出，但當時人們對於蛋白質在機體中的核心作用並不了解。1926 年，詹姆斯・B・薩姆納揭示尿素酶是蛋白質，首次證明了酶是蛋白質。
第一個被定序的蛋白質是胰島素，由弗雷德里克・桑格完成，他也因此獲得 1958 年度的諾貝爾化學獎。首先被解析的蛋白質結構包括血紅素和肌紅素的結構，所用方法為 X 射線晶體學；該工作由馬克斯・佩魯茨和約翰・肯德魯於 1958 年分別完成，他們也因此獲得 1962 年度的諾貝爾化學獎。截至到 2017 年，蛋白質資料庫 (PDB) 中已存有接近 126,000 個原子級解析度的蛋白質及其相關錯合物的三維結構的坐標。
## 參見
## 參考文獻
## 外部連結
* （英文）蛋白質資料庫 （頁面存檔備份，存於網際網路檔案館）
* （英文）UniProt 上的蛋白質資源
* （英文）人類蛋白質圖集 （頁面存檔備份，存於網際網路檔案館）
* （英文）有關於蛋白質的超連結資訊（頁面存檔備份，存於網際網路檔案館）
* （英文）美國國家生物技術資訊中心中 Entrez 上的蛋白質資料庫 （頁面存檔備份，存於網際網路檔案館）
* （英文）美國國家生物技術資訊中心的蛋白質結構資料庫 （頁面存檔備份，存於網際網路檔案館）
* （英文）人類蛋白質參考資料庫
* （英文）人類蛋白質百科
* （英文）史丹福大學的 Folding@Home（頁面存檔備份，存於網際網路檔案館）
* （英文）蛋白質：生物合成降解 - 生物化學和細胞生物學的虛擬圖書館
* （英文）胺基酸的代謝 （頁面存檔備份，存於網際網路檔案館） | [
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機率論 | **機率論**（英語：Probability theory）是研究機率、隨機性及不確定性等現象的數學分支。機率論主要研究物件為隨機事件、隨機變數以及隨機過程。
對於隨機事件是不可能準確預測其結果的，然而對於一系列的獨立隨機事件 —— 例如擲骰子、扔硬幣、抽撲克牌以及輪盤等，會呈現出一定的、可以被用於研究及預測的規律，兩個用來描述這些規律的最具代表性的數學結論分別是大數法則和中央極限定理。
作為統計學的數學基礎，機率論對諸多涉及大量數據定量分析的人類活動極為重要，機率論的方法同樣適用於其他方面，例如對只知道系統部分狀態的複雜系統的描述 —— 統計力學，而二十世紀物理學的重大發現是以量子力學所描述的原子尺度上物理現象的機率本質。
數學家和精算師認為機率是在 0 至 1 閉區間內的數字，指定給一發生與失敗是隨機的「事件」。機率 $P(A)$ 根據機率公理來指定給事件 $A$ 。
一事件 $A$ 在一事件 $B$ 確定發生後會發生的機率稱為 $B$ 給之 $A$ 的條件機率；其數值為 ${P(B\cap A) \over P(B)}$ 。若 $B$ 給之 $A$ 的條件機率和 $A$ 的機率相同時，則稱 $A$ 和 $B$ 為獨立事件。且 $A$ 和 $B$ 的此一關係為對稱的，這可以由一同價敘述：「當 $A$ 和 $B$ 為獨立事件時， $P(A\cap B)=P(A)P(B)$ 。」中看出。
機率論中的兩個重要概念為隨機變數和隨機變數的機率分布兩種。
## 生活例子
人們對機率總是有一點觸摸不清的感覺，而事實上也有很多看似奇異的結果：
* 六合彩：在六合彩（49 選 6）中，一共有 13,983,816 種可能性（參閱組合數學），如果每周都買一組不相同的號，一年有 52 周，則在實驗越多次（一直買直到中獎算一次）之後，平均中獎所花的時間會越接近 ${\frac {13983816}{52}}=268919$ 。
: 事實上，即使每周買相同的號碼，獲得頭獎的機率也是相同的。但假設每周實際中獎的組合都不重複，268919 年的算術推論是正確的，這說明機率和其他數學理論可能導出不同的結論。
* 六合彩：仍然是六合彩。買 5, 17, 19, 24, 33, 49 中奬機率高還是買 1,2,3,4,5,6 的中奬機率高？
: 古典機率論說：一樣。 | [
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] |
機率論 | : 但實際上機械或彩球製造上都有些微小的差異，所以每組機率不一定完全相同，但必須累積多期開獎結果後才看得出來。
* 生日悖論：根據機率論，在每 23 人當中，至少有兩個人的生日相同的機率大於 50％。
* 輪盤遊戲：在遊戲中玩家可能認為，在連續出現多次紅色後，出現黑色的機率會越來越大。
: 這種判斷也是錯誤的，即出現黑色的機率每次是相等的，因為球本身並沒有「記憶」，它不會意識到以前都發生了什麼，其機率始終是 ${\frac {18}{37}}$ 。
: 但輪盤的前後期開獎數字形成時間序列（可能存在自我迴歸模型）。
* 三門問題：在參賽者面前有三扇關閉的門，其中只有一扇後面有名車，而其餘的後面是山羊。
: 遊戲規則是，參賽者先選取一扇門，但在他打開之前，主持人在其餘兩扇門中打開了一扇有山羊的門，並詢問參賽者是否改變主意選擇另一扇門，以使贏得名車的機率變大。
: 正確的分析結果是，假如不管開始哪一扇門被選，主持人都打開其餘兩扇門中有山羊的那一扇並詢問參賽者是否改變主意，則改變主意會使贏得汽車的機率增加一倍。
## 歷史
作為數學統計基礎的機率論的創始人分別是法國數學家帕斯卡和費馬，其可追溯到公元 17 世紀。當時的法國宮廷貴族裡盛行著擲骰子遊戲，遊戲規則是玩家連續擲 4 次骰子，如果其中沒有 6 點出現，玩家贏，如果出現一次 6 點，則莊家（相當於現在的賭場）贏。按照這一遊戲規則，從長期來看，莊家扮演贏家的角色，而玩家大部分時間是輸家，因為莊家總是要靠此維生的，而當時人們也接受了這種現象。
後來為了使遊戲更刺激，遊戲規則發生了些許變化，玩家這回用 2 個骰子連續擲 24 次，不同時出現 2 個 6 點，玩家贏，否則莊家贏。當時人們普遍認為，2 次出現 6 點的機率是一次出現 6 點的機率的 1 / 6，因此 6 倍於前一種規則的次數，也既是 24 次贏或輸的機率與以前是相等的。然而事實卻並非如此，從長期來看，這回莊家處於輸家的狀態，於是他們去請教當時的數學家帕斯卡，求助其對這種現象作出解釋。
其他對機率論的發展作出重要貢獻的人還有荷蘭物理、數學家惠更斯，瑞士物理、數學家伯努利，法國數學家棣美弗，法國數學、天文學家拉普拉斯，德國數學家高斯，法國物理、數學家卜瓦松，義大利數學、醫學家卡爾達諾以及蘇聯數學家科摩哥洛夫。
## 事件
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機率論 | 在一次隨機試驗中可能發生的不能再細分的結果被稱為基本事件，或者稱為單位事件，用 $E$ 表示。在隨機試驗中可能發生的所有單位事件的集合稱為事件空間，用 $S$ 來表示。例如在一次擲骰子的隨機試驗中，如果用獲得的點數來表示單位事件，那麼一共可能出現 6 個單位事件，則事件空間可以表示為 $S=\{1,2,3,4,5,6\}$ 。
上面的事件空間是由可數有限單位事件組成，事實上還存在著由可數無限以及不可數單位事件組成的事件空間，比如在一次獲得正面朝上就停止的隨機擲硬幣試驗中，其事件空間由可數無限單位事件組成，表示為： $S=$ {正，反正，反反正，反反反正，反反反反正，・・・}，注意到在這個例子中 "反反反正" 是單位事件。將兩根筷子隨意扔向桌面，其靜止後所形成的交角假設為 $\alpha $ ，這個隨機試驗的事件空間的組成可以表示為 $S=\{\alpha |0^{\circ }\leq \alpha <180^{\circ }\}$ 。
隨機事件是事件空間 $S$ 的子集，它由事件空間 $S$ 中的單位元素構成，用大寫字母 $A,B,C\cdots $ 表示。例如在擲兩個骰子的隨機試驗中，設隨機事件 $A$ = 「獲得的點數和大於 10」，則 $A$ 可以由下面 3 個單位事件組成： $A=\{(5,6),(6,5),(6,6)\}$ 。
如果在隨機試驗中事件空間中的所有可能的單位事件都發生，這個事件被稱為 必然事件，表示為 $S\subset S$ ；相應的如果事件空間裡不包含任何一個單位事件，則稱為不可能事件，表示為 $\varnothing \subset S$ 。
### 事件的計算
因為事件在一定程度上是以集合的含義定義的，因此可以把集合計算方法直接應用於事件的計算，也就是說，在計算過程中，可以把事件當作集合來對待。
在輪盤遊戲中假設 $A$ 代表事件「球落在紅色區域」， $B$ 代表事件 "球落在黑色區域"，因為事件 $A$ 和 $B$ 沒有共同的單位事件，因此可表示為
$$
A\cap B=\varnothing
$$
注意到事件 $A$ 和 $B$ 並不是互補的關係，因為在整個事件空間 $S$ 中還有一個單位事件「零」，其即不是紅色也不是黑色，而是綠色，因此 $A,B$ 的補集應該分別表示如下：
${\bar {A}}=S\setminus A=B\cup \left\{0\right\}$ | [
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機率論 | ${\bar {B}}=S\setminus B=A\cup \left\{0\right\}$
## 機率的定義
### 傳統機率 (古典機率)(拉普拉斯機率)
傳統機率的定義是由法國數學家拉普拉斯 (Laplace) 提出的。如果一個隨機試驗所包含的單位事件是有限的，且每個單位事件發生的可能性均相等，則這個隨機試驗叫做拉普拉斯試驗。在拉普拉斯試驗中，事件 $A$ 在事件空間 $S$ 中的機率 $P(A)$ 為：
:
例如，在一次同時擲一個硬幣和一個骰子的隨機試驗中，假設事件 $A$ 為獲得國徽面且點數大於 4 ，那麼事件 $A$ 的機率應該有如下計算方法： $S=$ {( 國徽，1 點)，(數字，1 點)，(國徽，2 點)，(數字，2 點)，(國徽，3 點)，(數字，3 點)，(國徽，4 點)，(數字，4 點)，(國徽，5 點)，(數字，5 點)，(國徽，6 點)，(數字，6 點) }， $A$ ＝{(國徽，5 點)，(國徽，6 點)}，按照拉普拉斯定義， $A$ 的機率為，
: $P(A)={\frac {2}{12}}={\frac {1}{6}}$
注意到在拉普拉斯試驗中存在著若干的疑問，在現實中是否存在著其單位事件的機率具有精確相同的機率值的試驗？因為我們不知道，硬幣以及骰子是否完美，即骰子製造的是否均勻，其重心是否位於正中心，以及輪盤是否傾向於某一個數字。
儘管如此，傳統機率在實踐中被廣泛應用於確定事件的機率值，其理論根據是：
如果沒有足夠的論據來證明一個事件的機率大於另一個事件的機率，那麼可以認為這兩個事件的機率值相等。
如果仔細觀察這個定義會發現拉普拉斯用機率解釋了機率，定義中用了相同的可能性 (原文是 également possible) 一詞，其實指的就是 "相同的機率"。這個定義也並沒有說出，到底什麼是機率，以及如何用數字來確定機率。在現實生活中也有一系列問題，無論如何不能用傳統機率定義來解釋，比如，人壽保險公司無法確定一個 50 歲的人在下一年將死去的機率。
### 統計機率 | [
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機率論 | 繼傳統機率論之後，英國邏輯學家約翰・維恩和奧地利數學家理察提出建立在頻率理論基礎上的統計機率。他們認為，獲得一個事件的機率值的唯一方法是通過對該事件進行 100 次，1000 次或者甚至 10000 次的前後相互獨立的 $n$ 次隨機試驗，針對每次試驗均記錄下絕對頻率值 $h_{n}$ (A) 和相對頻率值 $f_{n}$ (A)，隨著試驗次數 $n$ 的增加，會出現如下事實，即相對頻率值會趨於穩定，它在一個特定的值上下浮動，也即是說存在著一個極限值 $P(A)$ ，相對頻率值趨向於這個極限值。這個極限值被稱為統計機率，表示為：
: $P(A)=\lim _{n\to \infty }f_{n}(A)$
例如，若想知道在一次擲骰子的隨機試驗中獲得 6 點的機率值可以對其進行 3000 次前後獨立的扔擲試驗，在每一次試驗後記錄下出現 6 點的次數，然後通過計算相對頻率值可以得到趨向於某一個數的統計機率值。
上面提到的這個有關相對頻率的經驗規律是大數法則在現實生活中的反映，大數法則是初等機率論的基礎。統計機率在今天的實踐中依然具有重要意義，特別是在初等機率論及數理統計等學科中。
### 現代機率論
與初等機率論相對的，是「現代機率論」。因「測度論」的研究與發展，現代機率論得以建立公理化系統。一些曾經無法用初等機率論解釋的概念因此得以用公理化的語言進行解釋，可以說現代機率論以測度論為理論基礎終於得以完善，完成了其現代化進程。現代機率論由前蘇聯數學家科摩哥洛夫於 1933 年建立公理化。
## 機率公理
如果一個函數 $P:S\to \mathbb {R} ,\ A\mapsto P(A)$ 指定給每一個事件空間 $S$ 中的事件 $A$ 一個實數 $P(A)$ ，並且其滿足下面的 3 個公理，那麼函數 $P$ 叫做機率函數，相應的 $P(A)$ 叫做事件 $A$ 的機率。
## 完全機率
$n$ 個事件 $H_{1},H_{2},...H_{n}$ 兩兩互斥，且共同組成整個事件空間 $S$ ，即
$H_{i}\cap H_{j}=\varnothing $ ， $(i\neq j)$ 以及
$H_{1}\cup H_{2}\cup ...\cup H_{n}=S$
這時 $A$ 的機率可以表示為，
: $P(A)=\sum _{j=1}^{n}P(A|H_{j})\cdot P(H_{j})$ | [
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機率論 | 例如，一個隨機試驗工具由一個骰子和一個柜子中的三個抽屜組成，抽屜 1 里有 14 個白球和 6 個黑球，抽屜 2 里有 2 個白球和 8 個黑球，抽屜 3 里有 3 個白球和 7 個黑球，試驗規則是首先擲骰子，如果獲得小於 4 點，則抽屜 1 被選擇，如果獲得 4 點或者 5 點，則抽屜 2 被選擇，其他情況選擇抽屜 3 。然後在選擇的抽屜里隨機抽出一個球，最後抽出的這個球是白球的機率是：
P (白)=P (白 | 抽 1)・P (抽 1)+P (白 | 抽 2)・P (抽 2)＋P (白 | 抽 3)・P (抽 3)
: : =(14/20)·(3/6)+(2/10)·(2/6)+(3/10)·(1/6)
: =28/60=0.4667
從例子中可看出，完全機率特別適合於分析具有多層結構的隨機試驗的情況。
## 貝氏定理
貝氏定理由英國數學家托馬斯・貝葉斯 (Thomas Bayes 1702-1761) 發展，用來描述兩個條件機率之間的關係，比如 P (A|B) 和 P (B|A)。按照定理 6 的乘法法則，P (A∩B)=P (A)・P (B|A)=P (B)・P (A|B)，可以立刻導出貝氏定理：
: $P(A\vert B)={\frac {P(B\vert A)\cdot P(A)}{P(B)}}$
例如：一座別墅在過去的 20 年裡一共發生過 2 次被盜，別墅的主人有一條狗，狗平均每周晚上叫 3 次，在盜賊入侵時狗叫的機率被估計為 0.9，問題是：在狗叫的時候發生入侵的機率是多少？
我們假設 $A$ 事件為狗在晚上叫， $B$ 為盜賊入侵，則 $P(A)=3/7$ ， $P(B)$ =2/(20・365.25)=2/7305，P (A | B) = 0.9，按照公式很容易得出結果：
$P(B\vert A)=0.9\cdot {\frac {2}{7305}}\cdot {\frac {7}{3}}=0.0005749486653...$
另一個例子，現分別有 $A$ ， $B$ 兩個容器，在容器 $A$ 里分別有 7 個紅球和 3 個白球，在容器 $B$ 里有 1 個紅球和 9 個白球，現已知從這兩個容器里任意抽出了一個球，且是紅球，問這個紅球是來自容器 $A$ 的機率是多少？ | [
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機率論 | 假設已經抽出紅球為事件 $B$ ，從容器 $A$ 里抽出球為事件 $A$ ，則有： $P(B)$ = 8 / 20， $P(A)$ = 1 / 2， $P(B|A)$ = 7 / 10，按照公式，則有：
$P(A\vert B)={\frac {7}{10}}\cdot {\frac {1}{2}}\cdot {\frac {20}{8}}={\frac {7}{8}}$
## 機率分布
## 機率論的應用
雖然機率論最早產生於 17 世紀，然而其公理體系只在 20 世紀的 20 至 30 年代才建立起來並得到迅速發展，在過去的半個世紀裡機率論在越來越多的新興領域顯示了它的應用性和實用性，例如：物理、化學、生物、醫學、心理學、社會學、政治學、教育學，經濟學以及幾乎所有的工程學等領域。特別值得一提的是，機率論是今天數理統計的基礎，其結果被用做問卷調查的分析資料或者對經濟前景進行預測。
## 參見
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绝对零度 | 絕對零度（英語：absolute zero）是熱力學的最低溫度，是粒子動能低到量子力學最低點時物質的溫度，絕對零度是僅存於理論的下限值，其熱力學溫標寫成 0**K**，等於攝氏溫標零下 273.15 度（即−273.15℃）或華氏溫標零下 459.67 度（即−459.67℉）。物質的溫度取決於其內原子、分子等粒子的動能。根據馬克士威 - 波耳茲曼分佈，粒子動能越高，物質溫度就越高。理論上，若粒子動能低到量子力學的最低點時，物質即達到絕對零度，不能再低。然而，根據熱力學定律，絕對零度永遠無法達到，只可無限逼近。因為任何空間必然存有能量和熱量，也不斷進行相互轉換而不消失。所以絕對零度是不存在的，除非該空間自始即無任何能量熱量。在此一空間，所有物質完全沒有粒子振動，其總體積並且為零 (絕對真空)。
有關物質接近絕對零度時的行為，可初步觀察德布洛伊波長。定義如下：
: $\lambda _{th}\equiv {\frac {h}{\sqrt {2\pi mkT}}}$
其中 $h$ 為普朗克常數、 $m$ 為粒子的質量、 $k$ 為波茲曼常數、 $T$ 為絕對溫度。可見熱德布洛伊波長與絕對溫度的平方根成反比，因此當溫度很低的時候，粒子物質波的波長很長，粒子與粒子之間的物質波有很大的重疊，因此量子力學的效應就會變得很明顯。著名的現象之一就是在 1995 年首次被實驗證實的玻色 - 愛因斯坦凝聚，當時溫度降至只有 1.7×10-7 K .
## 逼近絕對零度的方法
和外太空宇宙背景輻射的 3K 溫度做比較，實現玻色 - 愛因斯坦凝聚的溫度 1.7×10-7K 遠小於 3K，可知在實驗上要實現玻色 - 愛因斯坦凝聚是非常困難的，因為這代表著我們需要將溫度降到宇宙背景輻射之下，而目前僅知在整個可知宇宙環境中只有回力棒星雲之溫度符合該條件，而造成該星雲溫度如此之低的原因之一為絕熱膨脹。要製造出如此極低的溫度環境，主要的技術是雷射冷卻和蒸發冷卻。
* 雷射冷卻
* 蒸發冷卻
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绝对零度 | 在常用的攝氏或華氏溫標下，以負數形式表示的溫度只是單純的比此兩種表示方式下的零數值溫度更低的溫度。然而某些熱力學系統是可以達到真正意義上的負溫度的，換句話說，這些系統在熱力學定義下的溫度（以熱力學溫標 K 表示）可以是一個負的值。一個具有負溫度的系統並不是說它比絕對零度更冷。恰恰相反，從感官上來講，具有負溫度的系統比任意一個具有正溫度的系統都更熱一些。當分別具有正負溫度的兩個系統接觸時，熱量會由負溫度系統流向正溫度系統。
大多數常見的系統都無法達到負溫度，因為增加能量也會使得它們的熵增加的。但是，某些系統能夠持有的能量是有上限的，當能量達到這個上限時，它們的熵實際上會減少。因為溫度是由能量和熵之間的關係來定義的，所以即使能量在不停的增加，這個系統的溫度仍會變成負值。所以，當能量增加時，對於處於負溫度的系統，描述其狀態的波茲曼因子會增大而不是減小。因此，沒有一個完備的系統 —— 包括電磁系統 —— 能夠達到負溫度，這是因為能量狀態不會達到最大，所以不會有負溫度出現。但是，對於準均衡系統（如因自旋而導致不均衡的電磁場）這一理論並不適用，所以準均衡系統是可能達到負溫度的。
2013 年 1 月 3 日，有物理學家聲稱首次製造出了高等自由態的負溫度系統，該系統是由鉀原子組成的量子氣體。
## 參見
* 溫度
* 熱力學
* 普朗克溫度
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气温 | **溫度**是表示物體冷熱程度的物理量，微觀上來講是物體分子熱運動的劇烈程度。溫度只能通過物體隨溫度變化的某些特性來間接測量，而用來量度物體溫度數值的標尺叫溫標。它規定了溫度的讀數起點（零點）和測量溫度的基本單位。溫度理論上的高極點是「普朗克溫度」，而理論上的低極點則是「絕對零度」。「普朗克溫度」和「絕對零度」都是無法通過有限步驟達到的。目前國際上用得較多的溫標有攝氏溫標（°C）、華氏溫標（°F） 、熱力學溫標（K）和國際實用溫標。
溫度是物體內分子間平均動能的一種表現形式。值得注意的是，少數幾個分子甚至是一個分子構成的系統，由於缺乏統計的數量要求，是沒有溫度的意義的。
溫度出現在各種自然科學的領域中，包括物理、地質學、化學、大氣科學及生物學等。像在物理中，二物體的熱平衡是由其溫度而決定，溫度也會造成固體的熱漲冷縮，溫度也是熱力學的重要參數之一。在地質學中，岩漿冷卻後形成的火成岩是岩石的三種來源之一，在化學中，溫度會影響反應速率及化學平衡。大氣層中氣體的溫度是**氣溫**（atmospheric temperature），是氣象學常用名詞。它直接受日射所影響：日射越多，氣溫越高。
溫度也會影響生物體內許多的反應，恆溫動物會調節自身體溫，若體溫升高即為發熱，是一種醫學症狀。生物體也會感覺溫度的冷熱，但感受到的溫度受風寒效應影響，因此也會和周圍風速有關。
## 溫度計量
使用當代科學溫度計和溫度標記法進行溫度計量可以追溯到 18 世紀早期，加布里埃爾・華倫海特使用了奧勒・羅默發明的溫度計（轉換成了水銀）和標記方式。華氏溫標仍然在美國日常生活中使用。
使用溫度計標定的溫度可以通過溫度換算轉換為多種溫度計量法。在當今世界大多數國家（除了貝里斯、緬甸、賴比瑞亞和美國外），攝氏溫標是最為廣泛的計量法。大多數科學家使用攝氏溫標，並在熱力學溫度上使用攝氏溫標演化出來的熱力學溫標，其起始點 0K = −273.15°C（絕對零點）。在美國，工程領域、高科技行業以及美國聯邦規格（民用和軍用）上也會使用熱力學溫標和攝氏溫標。在美國的其他一些工程領域，針對諸如燃燒等熱力學相關標準時也會使用蘭金溫標（對華氏溫標的調整）。
### 單位
在國際單位制中，溫度的最基本單位是克耳文，其符號為 K。 | [
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气温 | 在日常使用中，一般為了方便起見都會將其轉換為攝氏溫標，其中 0°C 接近水的冰點，100°C 則為水在海拔 0M 的沸點。由於液態的水滴會出現在低於零度的雲層中，因此 0°C 更好的定義是冰的融化點。在這種溫標下，1 攝氏度和 1K 溫度變化是一樣的。
根據國際協議，熱力學溫標和攝氏溫標都通過兩個固定點定義：維也納標準平均海水的絕對零度和三相點。絕對零度被定義為 0K 及−273.15°C。在該溫度下，所有古典分子運動都會停止，處於古典模型下的完全靜止狀態。在量子結構下，在絕對零度下仍然有運動和能量，被稱為零點能量。物質處於其基態，不包含熱能。水的三相點則被定義為 273.16K 和 0.01°C。
而美國廣泛使用的華氏溫標中，水的冰點為 32 °F，沸點為 212 °F。
#### 轉換
下面的表格展示了各溫標如何轉換為攝氏溫標。
## 溫度對自然的影響
溫度對音速、空氣密度、聲阻抗有顯著影響。
## 溫度範例
* **A** 維也納標準平均海水在一個標準大氣壓（101.325 kPa）下，根據熱力學溫度兩點的定義。
* **B** 2500 K 值為約數，在熱力學溫標和攝氏溫標之間 273.15 K 的差值被約為 300 K，以避免攝氏度值的假精確問題。
* **C** 針對一個真正的黑體（鎢燈絲並不是）。鎢燈絲的輻射比短波要略長，因此看起來更白。
* **D** 有效光球溫度。在熱力學溫標和攝氏溫標之間 273.15 K 的差值被約為 273 K，以避免攝氏度值的假精確問題。
* **E** 在熱力學溫標和攝氏溫標之間 273.15 K 的差值已經忽略不計。
* **F** 針對一個真正的黑體（電漿並不是）。
## 溫度測量
由於溫度會對體積、密度、聲速、阻抗等物理量產生影響，因此可以通過測量這些物理量數值的變化來測量溫度。目前溫度測量的方法有數十種，按照測量原理可以分為以下幾類：
* 膨脹測溫法，是採用幾何量 (體積、長度) 作為溫度的標誌。如水銀溫度計的測量範圍大約是－30～300°C，酒精溫度計的測量範圍大約是 - 115～110℃，
* 電學測溫法，是採用某些隨溫度變化的電阻等電學量作為溫度的標誌。電阻溫度計多用於低於 600℃的場合，熱電偶溫度計測量範圍一般在 1600℃以下，此外還有半導體熱敏電阻溫度計。
* 磁學測溫法，是根據順磁物質的磁化率與溫度的關係來測量溫度，常用在超低溫（小於 1K）測量中。 | [
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] |
气温 | * 聲學測溫法，採用聲速作為溫度標誌（聲速的平方與溫度成正比）。主要用於低溫下熱力學溫度的測定。
* 頻率測溫法，根據物體固有頻率的變化來測量溫度。石英晶體溫度計的解析度可達萬分之一攝氏度。
* 光學測溫法，是根據黑體輻射來測量溫度。如紅外線溫度計。
* 密度測溫法，如伽利略溫度計。
## 參考資料
## 外部連結 | [
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中子 | **中子**（英語：Neutron）是一種電中性的粒子，具有略大於質子的質量。中子屬於重子類，由兩個下夸克、一個上夸克和用於在它們三者之間作用的膠子共同構成。夸克的靜質量只貢獻出大約 1% 質子質量，剩餘的質子質量主要源自於夸克的動能與綑綁夸克的膠子場的能量。絕大多數的原子核都由中子和質子組成（僅有氫 - 1 例外，它僅由一個質子構成）。在原子核外，自由中子性質不穩定，平均壽命約 877.75 秒。中子衰變時釋放一個電子和一個反微中子而成為質子（β 衰變）。同樣的衰變過程在一些原子核中也存在。原子核中的中子和質子可以通過吸收和釋放 π 介子互相轉換。中子是由劍橋大學卡文迪許實驗室的英國物理學家詹姆斯・查德威克於 1932 年發現的。
以往曾經將中子列為基本粒子的一員。但現今在標準模型理論下，因為中子是由夸克組成，所以它是個複合粒子。
中子和其它常見的次原子粒子最大的分別在於中子因其下夸克和上夸克之電荷互相抵消，因此中子帶電中性。另它穿透性強，無法直接進行觀察，也令它在核轉變中成為非常重要的媒介物。這兩項因素使得它在次原子粒子發展歷史的較後期才被發現。
雖然組成物質的原子在正常情況下呈電中性，但原子比中子大十萬倍，是由帶負電的電子圍繞帶正電的原子核運行而形成的複雜系統。帶電粒子（如質子，電子，或離子）和電磁波（如伽瑪射線）都會在穿透物質時消耗能量，形式是將所穿透物質離子化。帶電粒子會因此而慢下來，電磁波則會被所穿透物質吸收。中子的情況截然不同，它只會在與原子核近距離接觸時受強交互作用或弱交互作用影響：結果一個自由中子在與原子核直接碰撞前不受任何外力影響。因為原子核太小，碰撞機會極少，因此自由中子會在一段極長的距離保持不變。
自由中子和原子核的碰撞是彈性碰撞，其遵循巨觀下兩小球彈性碰撞時的動量法則。當被碰撞的原子核很重時，原子核只會有很小的速度；但是，若是碰撞的對象是和中子質量差不多質子，則質子和中子會以幾乎相同的速度飛出。這類的碰撞將會因為製造出的離子而被偵測到。 | [
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中子 | 中子的電中性讓它不僅很難偵測，也很難被控制。電中性使得我們無法以電磁場來加速、減速或是束縛中子。自由中子僅對磁場有很微弱的作用（因為中子存在磁矩）。真正能有效控制中子的只有核作用力。我們唯一能控制自由中子運動的方式只是放置原子核堆在它們的運動路徑上，讓中子和原子核碰撞藉以吸收之。這種以中子撞擊原子核的反應在核反應中扮演重要角色，也是核子武器運作的原理。自由中子則可由核衰變、核反應或高能反應等中子源產生。
物理學中有專門的中子學、中子物理學。
## 中子的發現
1920 年，歐尼斯特・拉塞福首先提出了中子存在的可能性。拉塞福假設，一種原子的原子量同其原子序數的差別可以用原子核中存在一種電中性粒子來解釋。他認爲，這種電中性的粒子是由一個電子環繞一個質子構成。
1920 年代，當時物理學者公認的原子核模型是原子核由質子構成。但是，當時已經知道一種原子的原子核只帶有大概其原子量一半的正電荷。對這個現象的解釋是原子核中有一些電子，中和了質子的電荷。以氮 - 14 核為例：當時認爲此原子核由 14 個質子和 7 個核外電子構成。因此，它應該帶 7 個正電荷，同時質量數為 14。
隨後興起的量子力學指出，任何能量也無法把電子這樣輕的粒子束縛在像原子核這樣小的區域中。1930 年，前蘇聯的維克托・安巴楚勉和迪米特裏・伊瓦年科發現原子核不可能只由質子和電子組成；有某種中性的粒子存在於原子核中。
1931 年，德國物理學者瓦爾特・博特和赫伯特・貝克爾發現用釙的高能 α 粒子轟擊鈹、硼或鋰這些較輕的元素，會產生一種貫穿力極強的輻射。開始他們認爲這種輻射是伽馬射線。但是未知輻射比任何已知伽馬射線貫穿力都強，而且實驗結果很難用伽馬射線來解釋。1932 年，伊雷娜・約里奧 - 居禮和弗雷德里克・約里奧 - 居禮在巴黎發現，如果用這種未知輻射照射石蠟和其他富含氫的化合物，就會釋放出高能質子。雖然這個結果同高能伽馬射線一致，但細緻的數據分析表明未知輻射是伽馬射線的假説越來越牽強。
1932 年，英國物理學家詹姆斯・查德威克在劍橋大學進行了一系列的實驗，以 α 粒子轟擊硼 - 10 原子核得到氮 - 13 原子核和一種新射線，證明伽馬射線假說站不住腳。他提出這種新輻射是一種質量近似於質子的中性粒子，並設計了實驗證實了他的理論。這種中性粒子被稱作中子。
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中子 | 在查兌克發現中子以前，流行的原子核模型為「質子 - 電子」模型。但這個模型存在很多的問題。比如，在氮氣（N2）的分子光譜中，偶數轉動能級的越遷要比奇數轉動能級的強烈，這説明偶數能級上的集居數比奇數能級的大。根據量子力學和包立不相容原理，這意味著 N-14 核的自旋是約化普朗克常數ħ（普朗克常數除以 2π）的整數倍。這個結果同質子 - 電子模型相悖。質子和電子的自旋皆為 1⁄2ħ。如果一個氮核由 14 個質子同 7 個電子組成，無論怎樣組合也無法得到其自旋是ħ的整數倍。
中子 - 質子模型能夠很好地解決這個問題。從 β 衰變中，費米得出結論說中子的自旋也必須是 ±1⁄2ħ，否則該反應的角動量就不守恆。如果 N-14 核由三個中子 - 質子對加上一對自旋方向相同但不配對的中子和質子構成，其自旋恰恰為 1ħ。這一理論很快被用到其它核種上。
另外，原子光譜中通常會有由原子核引起的超精細結構。這一結構不受電子的自旋影響。這也和質子 - 電子模型相矛盾。因爲如果原子核中有電子的話，電子的自旋反轉勢必會導致超精細結構的變化。最終人們意識到，除質子外，原子核中不存在電子，而存在一種中性的粒子，那就是中子。人們很快就接受了原子核是由質子和中子組成的。
## 性質
### 穩定性和 β 衰變
中子由三個夸克構成。根據標准模型，爲了保持重子數守恆，中子唯一可能的衰變途徑是其中一個夸克通過弱交互作用改變其味。組成中子的三個夸克中，兩個是下夸克（電荷−1⁄3e），另外一個是上夸克（電荷 +2⁄3e）。一個下夸克可以衰變成一個較輕的上夸克，並釋放出一個 W 玻色子。這樣中子可以衰變成質子，同時釋放出一個電子和一個反電子微中子。
#### 自由中子的衰變
自由中子不穩定，其平均壽命為 881.5±1.5 秒（大概 14 分鐘 42 秒）。據此估計其半衰期為 611.0±1.0 秒（大概 10 分鐘 11 秒）。中子的衰變可用以下方程式描述：
: n0
→
p+
+
e−
+
ν
e
根據微中子、質子和電子的質量，此反應的衰變能為 0.782343 百萬電子伏特。如果此反應中微中子的動能忽略不計的話，已測得電子的最大能量為 0.782±.013 百萬電子伏特。這一實驗結果誤差太大，無法用於估計微中子的靜止質量。
有千分之一的自由中子會在生成質子、電子和微中子的同時，釋放出 γ 射綫：
: n0
→
p+
+
e−
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] |
中子 | ν
e +
γ
這種 γ 射綫是軔致輻射的結果。當反應中釋放出的電子在質子產生的電磁場中運動時，高速運動的電子驟然減速發出的輻射。有時原子核中束縛態的中子衰變時，也會產生 γ 射綫。
有極少量的自由中子（大概百萬分之四）會發生所謂的雙體衰變。在此反應中，電子在產生後未能獲得足夠的能量脫離質子（估計為 13.6 電子伏特），於是和質子生成一個中性的氫原子。反應的所有能量皆轉化為反電子微中子的動能。
#### 束縛態中子的衰變
不穩定原子核裏的中子可以像自由中子一樣衰變。但是，中子衰變的逆過程也可以發生，即逆 β 衰變。質子可以轉變為一個中子，同時放出一個正電子和一個電子微中子：
: p+
→
n0
+
e+
+
ν
e
質子還可以通過電子俘獲轉變成一個中子，同時放出一個電子微中子：
: p+
+
e−
→
n0
+
ν
e
理論上，核內中子俘獲正電子生成質子也是有可能的。但是，兩個因素對此過程不利。一方面原子核帶正電荷，因此同正電子同性相斥。另一方面正電子和電子相遇會發生湮滅。因此正電子俘獲事件的幾率很小。
因原子核內的中子受到其他因素的制約，穩定性和自由中子不盡相同。比如，如果核內一個中子衰變成質子，核內正電荷的斥力就會增大。這個斥力的位能就變成中子衰變的一個勢壘。如果中子不能突破這個勢壘，它就無法衰變。這也可以解釋在自由狀態下穩定的質子有時會在束縛態中轉變為中子。
### 電偶極矩
標准模型預言中子具有微小但非零的電偶極矩。但是測量其數值所需的精度遠遠超過目前的實驗條件。標准模型不可能是對物理現實的最終和最完整的描述。超越標准模型的新理論得到的數值一般要比標准模型的大得多。目前，至少有四組實驗力圖測量中子的電偶極矩：
* 勞厄 - 朗之萬研究所（Institut Laue–Langevin）的低溫中子電偶極矩實驗（CryoEDM），在建
* 保羅・謝若研究所（Paul Scherrer Institute）的中子電偶極矩實驗（nEDM），在建
* 橡樹嶺國家實驗室散裂中子源（Spallation Neutron Source）的中子電偶極矩實驗（nEDM），擬建
* 勞厄 - 朗之萬研究所的中子電偶極矩實驗（nEDM），在建
### 磁矩
雖然中子是電中性粒子，但是中子具有微小但非零的磁矩。
### 反中子 | [
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] |
中子 | 反中子是中子的反粒子，是由布魯斯・考克（Bruce Cork）於 1956 年發現，比反質子的發現晚一年時間。CPT 對稱理論對粒子和反粒子的性質有嚴格的限制，因此觀測中子 - 反中子可以對 CPT 對稱進行縝密的檢驗。中子和反中子質量差異約為 (9±6)×10−5，僅為 2σ，不足以證明 CPT 對稱破缺。
### 中子結構和電荷的幾何分佈
一篇 2007 年發表的文章進行了不依賴於模型的分析後作出結論，中子的外殼帶負電荷，中間層帶正電荷，而中心帶有負電荷。簡單的說，中子的電負性外殼同質子相互吸引。但是，在原子核中，質子和中子之間最主要的作用力為核力。這種力跟粒子是否帶電荷無關。
## 中子復合物
### 雙中子穩定對和四中子穩定核
法國國家科學研究中心核物理實驗室的弗朗西斯科 - 米高兒・馬科斯（Francisco-Miguel Marqués）帶領的研究團隊在觀察鈹 - 14 核的裂變時，提出了四中子穩定核的假説。這一假説認爲，四個中子能形成一個穩定的原子核。現有理論認爲這種組合不穩定。後來的實驗工作未能重復馬科斯等人的發現。2016 年 2 月，日本東京大學物理學者下浦享（Susumu SHIMOURA）等發表論文稱，他們首次在實驗中觀測到了四中子穩定核的存在。 多名物理學者表示，如果這一工作得到證實，將是核物理學的重大發現，並加深我們對核力的理解。
此外，還有人認爲兩個中子也能形成一個穩定的對。斯皮尤等人稱在鈹 - 16 的衰變中首次觀測到了雙中子穩定對。
### 0 號元素和中子星
在極高溫度和壓力下，比如在大質量恆星的坍縮過程中，原子核中的質子可以和核外電子反應轉變為中子。最後的結果就是生成完全由中子構成的中子星。由於這種星體的巨大引力，有人提出其中的中子會被壓迫變形，成爲一種立方密堆積的結構，以獲得更高的堆積密度。
## 中子的檢測
檢測帶電粒子的最常見方式是尋找其電離徑跡，比如説在雲室中。但是這種檢測方式不能直接用於中子，因為它不帶電荷。如果中子和原子發生彈性碰撞，會產生觀察得到的電離徑跡。但這個實驗做起來並不容易。因此更常用的中子檢測是間接方式，比如中子俘獲和彈性散射。
### 中子俘獲
某些核種有很高的中子反應截面。它們在俘獲中子之後，會釋放出容易檢測的輻射，比如 α 粒子。常用於此目的的核種包括 3
He
, 6
Li
, 10
B
, 233
U
, 235
U
, 237
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] |
中子 | 和 239
Pu
。但中子反應截面一般同中子的能量有關。通常高能中子（快中子）的反應截面要低於低能中子（熱中子）。爲了增加反應截面，在檢測高能中子之前需要使中子減速。富含氫的化合物，比如聚乙烯，可以用作中子減速劑。但經過減速之後，中子的能量、到達時間以及入射角皆已不可測量。
### 彈性散射
中子可以和原子核發生彈性碰撞，使原子核在相反方向上發生運動。中子和原子核發生碰撞時，較輕的原子核能夠獲得更大的動能。用彈性散射來檢測中子的儀器稱爲快中子檢測器。受到正碰的原子核可以電離或撞擊其它物質，產生的電荷和閃爍光子可以很容易偵測到。快中子檢測器最主要的問題是如何區別入射輻射是 γ 射綫還是中子，因爲二者可以產生類似的結果。快中子檢測器不需要減速劑，因此可以測定中子的能量、到達時間以及入射角。
## 中子的產生和中子源
自由中子因爲半衰期比較短（10 分鐘 11 秒），因此只能現制現用。某些放射性衰變（比如自發裂變和中子發射）以及一些反應爐可以用於產生中子。某些核反應，比如用自然產生的 α 粒子轟擊一些核種（主要是輕元素，比如鈹和氘）引發的核分裂亦可產生中子。一些高能量核反應，比如高能宇宙射綫爆發和粒子加速器中用高能粒子轟擊靶子使其原子核發生分裂，也能產生中子流。一些小型加速器經過優化後專門用於產生中子，被稱作中子發生器。
在實驗室中，最常用的中子源是某些衰變時釋放中子的核種。比如鐦 - 252（半衰期為 2.65 年）的自發裂變，100 個原子中有 3 個鐦原子核分裂時會釋放中子，每次裂變會平均產生 3.7 個中子。用 α 粒子轟擊鈹靶也可製造中子。一個較爲流行的系統由銻 - 124 和金屬鈹構成。將金屬銻置於反應爐中以中子活化，銻 - 123（天然豐度為 42.8%）便會轉化為銻 - 124，半衰期為 60.9 天。其優點是便於儲存和運輸。
高能宇宙射綫轟擊大氣層的上層不停地產生中子，可以在地面上探測到。在火星表面大氣濃厚到一定程度的地方，由宇宙射綫產生的中子更多。這些中子不但在火星表面直接造成自上而下的輻射危害，還能夠經地表反射後形成自下而上的輻射。這是火星載人航天計劃不能不考慮的一個問題。
在核融合反應爐中，自由中子是反應的副產品，但卻攜帶了巨大的動能。如果把這些動能轉化為人類可用的能源是一個重大的挑戰。這些自由中子還會製造出大量的中子激活產物，最後必須當作核廢料處理。
### 中子束和中子束的調製 | [
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中子 | 自由中子束可以通過中子源產生。研究者們可以去特殊研究機構使用其研究反應爐或散裂中子源。比如美國橡樹嶺國家實驗室就擁有公衆可以申請使用的散裂中子源。
因爲其電中性，中子很難加速、減速、聚焦或偏轉。對帶電粒子可以用電場和磁場實現上述操作。但這些手段對中子影響不大。但因爲中子擁有微小但非零的磁矩，非均勻磁場可以起到一些控制作用。中子還可以通過減速、反射和速度選擇來來控制。如同光子的法拉第效應，熱中子通過磁性材料後可以被偏振化。通過使用磁鏡和磁性干涉濾鏡，可以製成極高偏振度（degree of polarization，中子波的偏振部分所佔有的百分比）、波長為 6-7 Å 的冷中子束。
## 中子的用途
中子在很多核反應中扮演重要角色。比如，許多核種可以俘獲中子，生成活化產物。對於反應爐和核武器的設計來說，對中子的了解極為重要。鈾 - 235 和鈈 - 239 的裂變也是由中子引發的。在對凝聚態物質的分析中，中子和 X 射線的散射反應截面、對磁場的敏感程度和貫穿能力可以相互補充。
利用中空玻璃纖維的全反射或者表面帶有凹陷的鋁板的反射，可以製成中子透鏡。這種透鏡有可能可以用於中子顯微鏡和中子／ϒ 射線斷層掃描照相。
中子的另一個主要用途是照射材料使之產生 ϒ 射線。這是中子活化分析的理論基礎。中子活化分析是一種高靈敏度的痕量分析方法。如果用高通量中子流（如核反應爐中，通量約為 1011~1014n.cm-2.sec-1）約可檢測至 0.1 ppb 的濃度。加速器所生的低通量快中子也可檢測約 1 ppm 濃度。實際應用中，檢測靈敏度應隨實驗的條件以及被測核種而有所不同。中子活化分析還很少需要或不需要樣品製備環節，對於複雜物質的分析得心應手。最後，中子活化分析是一種「無損」分析法，可以做表面和微區分析，因此可以用來分析古董、藝術品以及法醫鑑定。這種分析方法是 1936 年由喬治・德・海韋西（George Hevesy）和希爾德・李維（Hilde Levi）首創。瞬發中子活化分析具有快速、原位、不需要取樣等特點，可以用於打井時地下岩芯和工業傳送帶上物品的原位分析，並且是監測爆炸物，尤其是非金屬類爆炸物的有效手段之一。
中子還可以用來檢測輕核的存在，比如水分子中的氫核。快中子和輕核碰撞時會損失大部分能量。通過測量被氫核減速後的中子，可以測定土壤中的含水量。
## 中子的防護：慢化與屏蔽 | [
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中子 | 自由中子可以給生物體造成重大的傷害。中子不但能夠對生物大分子（比如 DNA）造成直接的損傷，還能夠引發次生輻射，比如質子和 ϒ 射線等。因此，輻射防護的基本原則也適用於中子的防護：應盡量避免暴露，盡量遠離中子源，縮短曝光時間。對於 α 射線、β 射線和 γ 射線，重元素製成的材料通常可以屏蔽，最常用的是鉛板。但是，這對於中子並不奏效，因為元素對中子的吸收能力同其原子序數並沒有直接關係。
中子防護過程，需要注意中子和其他物質的交互作用主要是三種：
* 彈性散射：中子和其他原子發生了彈性碰撞，可失去一部分動量。因此，如果碰撞目標的質量很大（重原子核），那麼中子將原速率反彈。如果碰撞目標與其質量相近（氫核），那麼中子可完全停下來，動量完全傳給碰撞目標（在電磁力作用下迅速減速）。彈性散射材料富含氫或其他低原子數核種的物質，如石蠟、石墨、混凝土、鈹、聚乙烯等。富含氫核的材料（比如水）會影響到裂變反應爐裡的中子吸收。輕水（正常水分子）對中子親和力很高，因此輕水堆必須使用濃縮後的裂變材料。重水（氘代替水中的氫核的產物）對熱中子的吸收截面是普通水的 1/6500，所以可以用於使用非濃縮核材料（天然鈾釷）的反應爐，比如坎杜反應爐（Canada Deuterium Uranium）。
* 非彈性散射：中子被其他原子核吸收成為一個複合核，短時間內又發出一個較低動能的中子，原子核進入激發態，隨後發射多個伽瑪光子。當原子的第一激發能越低越容易發生非彈性散射。而重核的第一激發能低。
* 中子俘獲：能量較低的中子被原子吸收後進入激發態，隨後輻射 伽瑪射線或阿爾法粒子、貝他粒子、質子等形式回到基態。鎘、硼 10 的中子俘獲能力強。鈹的熱中子俘獲截面小（對中子的散射截面大），所以常用這種散射物質做核反應爐的結構材料，以減少中子的逃逸與損失。
所以中子防護的順序是：
* 中子能量高時，以非彈性散射為主，應該先用重元素快速消耗快中子的能量；對於幾 MeV 以上的中子，可用含重核或中重核的材料，通過非彈性碰撞使其能量迅速降低
* 中子能量中等時，以彈性散射為主，應該用輕元素將中子慢化為熱中子；用含氫材料進一步使其慢化。富含氫核的材料卻可以用來屏蔽中子。混凝土或者鑲嵌有石蠟層的混凝土比重元素能夠更好的防護中子。屏蔽快中子最有效的元素是氫，常用材料是含氫成分較多的水、石蠟等。 | [
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中子 | * 中子能量低時，以中子俘獲為主，用鎘、硼 10 等吸收中子。中子防護必然有次生伽瑪射線輻射。利用 B10 或 Li6 等吸收截面大的物質，可使中子能量因原子核反應轉換成帶電粒子的能量，中子則被它們吸收。屏蔽熱中子用中子吸收截面大、俘獲 γ 光子能量低的材料，如硼、鋰及其化合物等。某些輕核種，比如鋰 - 6，可以吸收熱中子而不產生次生輻射。
中子的慢化過程，對於重核（A＞120）、中重核（40≤A≤120）—— 中子同核發生非彈性碰撞（散射），迅速降低能量；對於輕核（A＜40）—— 中子同核發生彈性碰撞（散射），減少能量。
## 中子的溫度
### 高能中子
高能中子是加速器轟擊靶子或高能宇宙射線轟擊大氣層所產生的次生粒子。其能量比快中子高得多。動能大於 10MeV。有的高能中子可以擁有數十焦耳的動能。它們具有極強的電離性能，比 X 射綫和質子更能造成細胞的損傷和死亡。
### 快中子
快中子是在核分裂反應中產生的自由中子，其動能 20keV～10MeV (1.6×10−13 焦耳，1MeV 對應的速度約為 14000 千米 / 秒，相當於光速的 5％。它們被稱作快中子，以區別於熱中子和宇宙射線或者加速器中產生的高能中子。核反應中產生的中子符合馬克士威 - 波茲曼分布，其能量在 0 到～14 百萬電子伏特之間。鈾−235 產生的中子平均能量為 2 百萬電子伏特，且超過一半的中子不是快中子。因此僅僅靠鈾−235 裂變產生的中子無法引發增殖性材料（比如鈾−238 和釷−232）的裂變。
快中子可以通過減速變成熱中子。在核反應爐中，通常使用輕水、重水、或石墨來使中子減速。
### 中能中子
能量介於快中子和熱中子之間的中子稱為中能中子。這種中子的能量在 100eV～20keV 之間。中子俘獲和核分裂的中子反應截面在這個能量區間有個多共振峰。中能中子在快中子堆和熱中子反應爐中並不重要。但在減速不良的熱中子反應爐中，中能中子可能引發連鎖反應反應性的變化，使得反應的控制更加困難。
某些核燃料吸收中子後並不一定裂變，比如鈽−239，這種性質可以用俘獲／裂變的比率來描述。因為俘獲事件不但浪費了一個中子，而且通常會生成熱中子或中能中子無法裂變的核。鈾−233 是個例外。對任何能量的中子，鈾−233 的俘獲／裂變比都很好。
### 慢中子
動能在 0-1000eV
### 高超熱中子
動能在 1000～100000eV
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中子 | 動能在 0.025eV～100eV
### 熱中子
熱中子是符合馬克士威 - 波茲曼分布並且其最可幾動能約為 kT = 0.0253 [[電子伏特]] (4.0×10−21[[焦耳]]) 的自由中子，對應這一動能的速率約為 2.2 千米 / 秒。這個速度也是對應於 290K（攝氏 17 度）時馬克士威 - 波茲曼分布下的最可幾速率。常溫下中子與介質的原子核發生若干次碰撞後，如果沒有被俘獲就會達到這個速率。熱中子通常有比快中子大得多的有效中子俘獲截面，也因此會更容易被原子核吸收，形成更重的、通常也不穩定的同位素。這個現像也被稱為中子活化。一些裂變反應爐藉助於減速劑實現對快中子的減速，也稱為「熱中子化」。在快中子增殖堆中，快中子被直接利用，沒有減速的步驟。
### 冷中子
把熱中子冷卻到極低溫度即得到冷中子，比如液氫或液氘。這樣的冷中子源一般放置在研究反應爐或散裂中子源的減速劑裡。冷中子源對於中子散射試驗非常重要。冷中子的能量約 5x10−5 電子伏特至 0.025 電子伏特之間。
### 甚冷中子
動能在 0.0001～0.0000001eV
### 超冷中子
冷中子通過與溫度只有幾 K 的物質（比如固體氘或者超流體液氦）發生非彈性散射後可以得到超冷中子。其能量小於 3x10−7eV。
## 核反應與中子
### 裂變中子
中子能量越大，轟擊原子核的裂變物質量分布對稱性越大。熱中子引發 U235 或 Pu239 裂變，其裂變產物包括一較輕的原子核與一較重的核，具有不對稱性，二者質量比是 2∶3，輕的分裂物集中在質量數 90～100 之間，較重分裂物集中在質量數 130～140 之間。鈾核分裂 1s 內它能產生 1000 代中子，每次裂變平均放出 2.5 個中子；1kg 純 U235，約經過 80 代中子就可全部裂變完。
1947 年錢三強在法國居禮研究院發現慢中子轟擊鈾核也有三分裂、四分裂現象，主要是二分裂；三分裂與二分裂之比是 0.003，四分裂與二分裂之比是 0.0003。 | [
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0.42480581998825073,
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0.08718224614858627,
0.15774331986904144,
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] |
中子 | 核分裂產生的中子叫裂變中子或分裂中子。又細分為瞬發中子和緩發中子（延遲中子），核分裂產生的大部分的中子在分裂瞬間（10-12s 內）放出，少數的則延遲放出。例如，U235、U233 和 Pu239 裂變時，瞬發中子占 99.2％，緩發中子占 0.8％。緩發中子平均能量在 1Mev 以下。 統計顯示，轟擊 U235，每次裂變放出的瞬發中子最多在 2～3 個之間，平均值為 2.4 個，釋放的中子的能量平均為 1.95MeV, 中子能量譜峰值在 0.8MeV 附近，其中緩發中子的能量平均在 300keV～500keV。14MeV 的中子引發 U235 裂變，放出的瞬發中子平均數為 4.4 個。
鉲 252 自發裂變也能產生大量的中子。是一種很好的中子源，其用途廣泛。
### 聚變中子
氘−氚（DT）融合反應產生能量較高的中子，動能為 14.1 百萬電子伏特，對應的速度相當於光速的 17％。這些中子是快中子能量的近 10 倍。氘−氚反應也是最容易點火的反應之一。在氘核和氚核的動能達到 14.1 百萬電子伏特的千分之一時，該反應就幾乎達到峰值反應速率。
聚變中子可以有效的引發不可裂變的重元素（比如錒系元素）的裂變，並釋放出更多的中子。因此，有人提議用將來的托卡馬克氘−氚融合反應堆來嬗變核廢料中的超鈾元素。散裂中子源也使用 14.1 百萬電子伏特的中子產生中子。
因為聚變中子不是引起裂變就是散裂，它難以被其它核吸收。氫彈核武器正是利用了這一特性。首先，融合反應產生高能量中子。下一步，不可裂變材料（比如鈾 - 238）在這些中子的轟擊下發生裂變。這很顯然帶來了一些核安全和擴散上的問題：如果有人掌握了融合反應，他們也許就可以用無法製造原子彈的核材料（比如貧化鈾和反應爐級鈈）製造熱核武器。
另外一些融合反應產生的中子能量較低。比如氘−氘（DD）聚變有 50％的幾率生成一個 2.45 百萬電子伏特的中子和一個氦 - 3 核；還有 50％的幾率生成氚核和一個質子。氘−氦−3（D-3He）聚變不生成中子。
## 中子彈
## 參考文獻
## 參見
* 複合粒子
* 粒子列表
* 核子
* 中子電偶極矩
* 0 號元素 | [
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半導體 | **半導體**（英語：Semiconductor）是一種電導率在絕緣體至導體之間的物質或材料。半導體在某個溫度範圍內，隨溫度升高而增加電荷載子的濃度，使得電導率上升、電阻率下降；在絕對零度時，成為絕緣體。依有無加入摻雜劑，半導體可分為：本徵半導體、雜質半導體（n 型半導體、p 型半導體）。
電導率容易受控制的半導體，可作為資訊處理的元件材料。從科技或是經濟發展的角度來看，半導體非常重要。很多電子產品，如電腦、行動電話、數位錄音機的核心單元都是利用半導體的電導率變化來處理資訊。常見的**半導體材料**有：第一代（另一種定義 / 說法：第一「類」）的矽、鍺，第二代（類）的砷化鎵、磷化銦，第三代（類）的氮化鎵、碳化矽等；而矽更是各種半導體材料中，在商業應用上最具有影響力的一種。
材料的導電性是由導帶中含有的電子數量決定。當電子從價帶獲得能量而跳躍至導電帶時，電子就可以在帶間任意移動而導電。一般常見的金屬材料其導電帶與價電帶之間的能隙非常小，在室溫下電子很容易獲得能量而跳躍至導電帶而導電，而絕緣材料則因為能隙很大（通常大於 9 電子伏特），電子很難跳躍至導電帶，所以無法導電。
一般半導體材料的能隙約為 1 至 3 電子伏特，介於導體和絕緣體之間。因此只要給予適當條件的能量激發，或是改變其能隙之間距，此材料就能導電。
半導體通過電子傳導或電洞傳導的方式傳輸電流。電子傳導的方式與銅線中電流的流動類似，即在電場作用下高度電離的原子將多餘的電子向著負離子化程度比較低的方向傳遞。電洞導電則是指在正離子化的材料中，原子核外由於電子缺失形成的「電洞」，在電場作用下，電洞被少數的電子補入而造成電洞移動所形成的電流（一般稱為正電流）。
材料中載子（carrier）的數量對半導體的導電特性極為重要。這可以通過在半導體中有選擇的加入其他「雜質」（IIIA、VA 族元素）來控制。如果我們在純矽中摻雜（doping）少許的砷或磷（最外層有 5 個電子），就會多出 1 個自由電子，這樣就形成 n 型半導體；如果我們在純矽中摻入少許的硼（最外層有 3 個電子），就反而少了 1 個電子，而形成一個電洞（hole），這樣就形成 p 型半導體（少了 1 個帶負電荷的原子，可視為多了 1 個正電荷）。
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半導體 | 半導體和絕緣體之間的差異主要來自兩者的能帶寬度不同。絕緣體的能帶比半導體寬，意即絕緣體價帶中的載子必須獲得比在半導體中更高的能量才能跳過能帶，進入導帶中。室溫下的半導體導電性有如絕緣體，只有極少數的載子具有足夠的能量進入導帶。因此，對於一個在相同電場下的本徵半導體和絕緣體會有類似的電特性，不過半導體的能帶寬度小於絕緣體也意味著半導體的導電性更容易受到控制而改變。
純質半導體的電氣特性可以藉由植入雜質的過程而永久改變，這個過程通常稱為摻雜。依照摻雜所使用的雜質不同，摻雜後的半導體原子周圍可能會多出一個電子或一個電洞，而讓半導體材料的導電特性變得與原本不同。如果摻雜進入半導體的雜質濃度夠高，半導體也可能會表現出如同金屬導體般（類金屬）的電性。在摻雜了不同極性雜質的半導體界面處會有一個內建電場（built-in electric field），內建電場和許多半導體元件的操作原理息息相關（例如太陽能電池電子與電洞對的蒐集就是靠內建電場來作用），而摻雜後的半導體有許多電性也會有相對應的變化。
除了藉由摻雜的過程永久改變電性外，半導體亦可因為施加於其上的電場改變而動態地變化。半導體材料也因為這樣的特性，很適合用來作為電路元件，例如電晶體。電晶體屬於主動式的（主動）半導體元件（active semiconductor devices），當主動元件和被動式的（無源）半導體元件（passive semiconductor devices）如電阻器或是電容器組合起來時，可以用來設計各式各樣的積體電路產品，例如微處理器。
當電子從導帶掉回價帶時，減少的能量可能會以光的形式釋放出來。這種過程是製造發光二極體以及半導體雷射的基礎，在商業應用上都有舉足輕重的地位。而相反地，半導體也可以吸收光子，透過光電效應而激發出在價帶的電子，產生電訊號。這即是光探測器的來源，在光纖通訊或是太陽能電池的領域是最重要的元件，也是相機中 CMOS Image Sensor 主要的運作原理。
半導體有可能是單一元素組成，例如矽。也可以是兩種或是多種元素的化合物，常見的化合物半導體有砷化鎵或是磷化鋁銦鎵（aluminium gallium indium phosphide, AlGaInP）等。合金也是半導體材料的來源之一，如矽鍺或是砷化鎵鋁（aluminium gallium arsenide, AlGaAs）等。
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半導體 | 在常溫下，半導體的電導率介於金屬導體（～ $10^{-9}$ S/m）和絕緣體（ $10^{-15}$ < S/m）之間，一般為 $10^{5}$ ～ $10^{-7}$ S/m 。
## 半導體的能帶結構
半導體中的電子所具有的能量被限制在基態與自由電子之間的幾個能帶裡，在能帶內部電子能量處於準連續狀態，而能帶之間則有帶隙相隔開，電子不能處於帶隙內。當電子在基態時，相當於此電子被束縛在原子核附近；而相反地，如果電子具備了自由電子所需要的能量，那麼就能完全離開此材料。每個能帶都有數個相對應的量子態，而這些量子態中，能量較低的都已經被電子所填滿。這些已經被電子填滿的量子態中，能量最高的就被稱為價電帶。半導體和絕緣體在正常情況下，幾乎所有電子都在價電帶或是其下的量子態裡，因此沒有自由電子可供導電。
半導體和絕緣體之間的差異在於兩者之間能帶間隙寬度不同，亦即電子欲從價帶跳入導電帶時所必須獲得的最低能量不一樣。通常能帶間隙寬度小於 3 電子伏特（eV）者為半導體，以上為絕緣體。
在絕對零度時，固體材料中的所有電子都在價帶中，而導電帶為完全空置。當溫度開始上升，高於絕對零度時，有些電子可能會獲得能量而進入導電帶中。導電帶是所有能夠讓電子在獲得外加電場的能量後，移動穿過晶體、形成電流的最低能帶，所以導電帶的位置就緊鄰價電帶之上，而導電帶和價電帶之間的差距即是能帶間隙。通常對半導體而言，能帶間隙的大小約為 1 電子伏特上下。在導電帶中，和電流形成相關的電子通常稱為自由電子。根據包利不相容原理，同一個量子態內不能有兩個電子，所以絕對零度時，費米能級以下的能帶包括價電帶全部被填滿。由於在填滿的能帶內，具有相反方向動量的電子數目相等，所以宏觀上不能載流。在有限溫度，由熱激發產生的導電帶電子和價電帶電洞使得導電帶和價電帶都未被填滿，因而在外電場下可以觀測到宏觀凈電流。
在價電帶內的電子獲得能量後便可躍升到導電帶，而這便會在價帶內留下一個空缺，也就是所謂的電洞。導電帶中的電子和價電帶中的電洞都對電流傳遞有貢獻，電洞本身不會移動，但是其它電子可以移動到這個電洞上面，等效於電洞本身往反方向移動。相對於帶負電的電子，電洞的電性為正電。
由化學鍵結的觀點來看，獲得足夠能量、進入導電帶的電子也等於有足夠能量可以打破電子與固體原子間的共價鍵，而變成自由電子，進而對電流傳導做出貢獻。 | [
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半導體 | 半導體和導體之間有個顯著的不同是半導體的電流傳導同時來自電子與電洞的貢獻，而導體的費米能階則已經在導帶內，因此電子不需要很大的能量即可找到空缺的量子態供其跳躍、造成電流傳導。
固體材料內的電子能量分布遵循費米 - 狄拉克分佈。在絕對零度時，材料內電子的最高能量即為費米能階，當溫度高於絕對零度時，費米能階為所有能階中，被電子占據機率等於 0.5 的能階。半導體材料內電子能量分布為溫度的函數也使其導電特性受到溫度很大的影響，當溫度很低時，可以跳到導電帶的電子較少，因此導電性也會變得較差。
### 能量 - 動量色散
上述關於能帶結構的內容為了簡化，因此跳過了一個重要的現象，稱為能量的色散（dispersion of energy）。同一個能帶內之所以會有不同能量的量子態，原因是能帶的電子具有不同波向量或者「_k - 向量_」。在 [學]] 中，_k - 向量_即為粒子的動量，不同的材料會有不同的能量 - 動量關係（_E-k_ relationship）。
能量 - 動量色散關係式能決定電子或電洞的等效質量（effective mass），以 $m^{*}$ 代表，公式如下：
: $m^{*}=\hbar ^{2}\cdot \left[{{d^{2}E(k)} \over {dk^{2}}}\right]^{-1}$
等效質量可視為聯繫量子力學與古典力學的一個參數。這個參數對於半導體材料而言十分重要，例如它和電子或電洞的遷移率（electrons or holes mobility）有高度關聯。電子或電洞的遷移率對於半導體元件的載子傳輸是相當基本的參數。
電子和電洞的等效質量不相等，這也造成了兩者的遷移率不同，進而讓「N - 通道」和「P - 通道」的金屬氧化物半導體場效電晶體導電性不同。
準確的說應該是動量變化為零，因為任何時候動量都是守恆的，不能說不必牽涉
半導體材料的導電帶底部和價電帶頂端在「能量 - 動量座標」上可能會處在不同的 k 值，這種材料叫做間接能帶材料（in-direct bandgap material），例如矽或是鍺。相對地，如果某種材料的導帶底部和價帶頂端有相同的 k 值，這種材料稱為直接能帶材料（direct bandgap material），最常見的例子是砷化鎵。電子在直接能隙材料的價帶與導帶的躍遷不涉及晶格動量的改變，因此發光的效率高過間接能隙材料甚多，砷化鎵也因此是光電半導體元件中最常見的材料之一。 | [
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半導體 | ## 載流子的產生與復合
當離子化的輻射能量落在半導體時，可能會讓價帶中的電子吸收到足夠能量而躍遷至導帶，並在價帶中產生一個電洞，這種過程叫做電子 - 電洞對的產生（generation of electron-hole pair）。而其他夠大的能量，如熱能，也可以同樣產生出電子 - 電洞對。
電子 - 電洞對則會經由復合的過程而被消滅。根據能量守恆的觀念，在導帶中的電子必須回到價帶，將所得到的能量釋放出來。能量釋放的形式包括熱能或輻射能，而這兩種能量量子化後的表徵分別是聲子以及光子。
對於處在穩態的半導體而言，電子 - 電洞對的產生與復合速率是相等的。而在一個已給定的溫度下，電子 - 電洞對的數量可由量子統計求得。量子力學處理此類問題時必須同時遵守能量以及動量守恆。
## 半導體的摻雜
半導體之所以能廣泛應用在今日的數位世界中，憑藉的就是其能藉由在本質半導體加入雜質改變其特性，這個過程稱之為摻雜。摻雜進入本質半導體的雜質濃度與極性皆會對半導體的導電特性產生很大的影響。而摻雜過的半導體則稱為雜質半導體。
### 摻雜物
哪種材料適合作為某種半導體材料的摻雜物需視兩者的原子特性而定。一般而言，摻雜物依照其帶給被摻雜材料的電荷正負被區分為施體（donor）與受體。施體原子帶來的價電子多會與被摻雜的材料原子產生共價鍵，進而被束縛。而沒有和被摻雜材料原子產生共價鍵的電子則會被施體原子微弱地束縛住，這個電子又稱為施體電子。和本徵半導體的價電子比起來，施體電子躍遷至導帶所需的能量較低，比較容易在半導體材料的晶格中移動，產生電流。雖然施體電子獲得能量會躍遷至導帶，但並不會和本徵半導體一樣留下一個電洞，施體原子在失去了電子後只會固定在半導體材料的晶格中。因此這種因為摻雜而獲得多餘電子提供傳導的半導體稱為 n 型半導體，n 代表帶負電荷的電子。
和施體相對的，受體原子進入半導體晶格後，因為其價電子數目比半導體原子的價電子數量少，等效上會帶來一個的空位，這個多出的空位即可視為電洞。受體摻雜後的半導體稱為 p 型半導體，p 代表帶正電荷的電洞。
以一個矽的本徵半導體來說明摻雜的影響。矽有四個價電子，常用於矽的摻雜物有三價與五價的元素。當只有三個價電子的三價元素如硼摻雜至矽半導體中時，硼扮演的即是受體的角色，摻雜了硼的矽半導體就是 p 型半導體。反過來說，如果五價元素如磷摻雜至矽半導體時，磷扮演施體的角色，摻雜磷的矽半導體成為 n 型半導體。 | [
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半導體 | 一個半導體材料有可能先後摻雜施體與受體，而如何決定此外質半導體為 n 型或 p 型必須視摻雜後的半導體中，受體帶來的電洞濃度較高或是施體帶來的電子濃度較高，亦即何者為此外質半導體的多數載流子（majority carrier）。和多數載流子相對的是少數載流子（minority carrier）。對於半導體元件的工作原理分析而言，少數載流子在半導體中的行為有著非常重要的地位。
## 半導體材料的製造
為了滿足量產上的需求，半導體的電性必須是可預測並且穩定的，因此包括摻雜物的純度以及半導體晶格結構的品質都必須嚴格要求。常見的品質問題包括晶格的位錯（dislocation）、孿晶面（twins）或是堆垛層錯（stacking fault） 都會影響半導體材料的特性。對於一個半導體元件而言，材料晶格的缺陷（晶體缺陷）通常是影響元件性能的主因。
目前用來成長高純度單晶半導體材料最常見的方法稱為柴可拉斯基製程（鋼鐵場常見工法）。這種製程將一個單晶的晶種（seed）放入溶解的同材質液體中，再以旋轉的方式緩緩向上拉起。在晶種被拉起時，溶質將會沿著固體和液體的介面固化，而旋轉則可讓溶質的溫度均勻。
## 全球半導體製造企業
* _爾必達於 2012 年 5 月宣告破產，2013 年 7 月由美光完成併購。_
### 全球十大半導體公司
截止到 2020 年 6 月，根據 TTM 對全球半導體公司收入的追蹤，整理出全球十大半導體公司（此列表僅限於直接或者通過美國或加拿大公開交易的公司，一般外國的公司會每半年提交報告一詞，因此滯後時間會更長，所有數據截止 2020 年 6 月 18 日，所有數據由 YCharts 提供 10 Biggest Semiconductor Companies（頁面存檔備份，存於網際網路檔案館）
## 應用
半導體元件可以通過結構和材料上的設計達到控制電流傳輸的目的，並以此為基礎構建各種處理不同訊號的電路。這是半導體在當前電子技術中廣泛應用的原因。
## 延伸閱讀
### 材料科學
* 導體
* 絕緣體
* 半導體材料
* PN 接面
### 物理學
* 固體物理學
* 物理化學
* 熱力學
* 電路學
* 電子學
* 積體電路
### 工業
* 半導體元件製造
## 參考來源
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] |
半導體 | * Muller, Richard S.; Theodore I. Kamins. Device Electronics for Integrated Circuits 2d. New York: Wiley. 1986. ISBN 978-0-471-88758-4.
* Sze, Simon M. Physics of Semiconductor Devices（2nd ed.）. John Wiley and Sons（WIE）. 1981. ISBN 978-0-471-05661-4.
: * 上冊：施敏；伍國珏；譯者：張鼎張、劉柏村。半導體元件物理學 (上冊). 臺灣：國立交通大學. 2008-08-01 [2008]. ISBN 978-986-843-951-1 （中文）. （繁體中文）
* 下冊：施敏；伍國珏；譯者：張鼎張、劉柏村。半導體元件物理學 (下冊). 臺灣：國立交通大學. 2009-04-14 [2009]. ISBN 978-986-843-954-2 （中文）. （繁體中文）
* Turley, Jim. The Essential Guide to Semiconductors. Prentice Hall PTR. 2002. ISBN 978-0-13-046404-0.
* Yu, Peter Y.; Cardona, Manuel. Fundamentals of Semiconductors : Physics and Materials Properties. Springer. 2004. ISBN 978-3-540-41323-3.
* Neamen, Donald A. Semiconductor Physics and Devices: Basic Principles (3rd ed.). McGraw-Hill Higher Education. 2003. ISBN 0-07-232107-5.
**引用**
## 相關條目
* 電子
* 電路
## 外部連結
* Howstuffworks' semiconductor page（頁面存檔備份，存於網際網路檔案館）
* US Navy Electrical Engineering Training Series | [
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] |
半導體 | * NSM-Archive（頁面存檔備份，存於網際網路檔案館） Physical Properties of Semiconductors
* Semiconductor Concepts at Hyperphysics（頁面存檔備份，存於網際網路檔案館）
* Principles of Semiconductor Devices（頁面存檔備份，存於網際網路檔案館） by Bart Van Zeghbroeck, University of Colorado
* Semiconductor OneSource Hall of Fame（頁面存檔備份，存於網際網路檔案館）、Glossary
* SiliconFarEast.com（頁面存檔備份，存於網際網路檔案館） What is a semiconductor?
### 半導體行業網站
* 半導體學院（頁面存檔備份，存於網際網路檔案館）
* 半導體技術天地
* 半導體
* 半導體. | [
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量子物理学 | **量子力學**（英語：Quantum mechanics）是物理學的分支學科。它主要描寫微觀的事物，與相對論一起被認為是現代物理學的兩大基本支柱，許多物理學理論和科學，如原子物理學、固態物理學、核物理學和粒子物理學以及其它相關的學科，都是以其為基礎。
19 世紀末，人們發現舊有的古典理論並沒有辦法解釋微觀系統，於是經由物理學家的努力，在 20 世紀初創立量子力學，解釋了這些現象。量子力學從根本上改變人類對物質結構及其交互作用的理解。除了透過廣義相對論描寫的引力外，迄今所有基本交互作用均可以在量子力學的框架內描述（量子場論）。
量子理論的重要應用包括宇宙學、量子化學、量子光學、量子計算、超導磁體、發光二極體、雷射器、電晶體和半導體如微處理器等。
愛因斯坦可能是在科學文獻中最先給出術語「量子力學」的物理學者。
## 關鍵現象、歷史背景
### 黑體輻射
理想黑體可以吸收所有照射到它表面的電磁輻射，並將這些輻射轉化為熱輻射，其光譜特徵僅與該黑體的溫度有關，與黑體的材質無關。從古典物理學出發推導出的維恩定律在低頻區域與實驗數據不相符，而在高頻區域，從古典物理學的能量均分定理推導出瑞立 - 金斯定律又與實驗數據不相符，在輻射頻率趨向無窮大時，能量也會變得無窮大，這結果被稱作「紫外災變」。然而在那時，普朗克並未注意到紫外災變的嚴重性。
1900 年 12 月 14 日，後來被定為量子力學的誕辰，馬克斯・普朗克在柏林科學院發表報告，通過將維恩定律加以改良，又將波茲曼熵公式重新詮釋，他得出了一個與實驗數據完全吻合的普朗克公式來描述黑體輻射，但是在詮釋這個公式時，他將在物體裡發射與吸收輻射的原子視為微小的量子諧振子，並且假設這些量子諧振子的能量不是連續的，而是離散的數值，並且單獨量子諧振子吸收和發射的輻射能是量子化的。
### 光電效應
海因里希・赫茲於 1887 年實驗發現，如果照射紫外光於金屬表面，則電子會從金屬表面被發射出來，他因此發現了光電效應。1905 年，阿爾伯特・愛因斯坦提出了光量子的理論來解釋這個現象。他認為，光束是由一群離散的光量子所組成，而不是連續性波動。這些光量子現今被稱為光子，其能量 $E$ 為
: $E=h\nu $
這裡， $\nu $ 是頻率， $h$ 為普朗克常數。 | [
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量子物理学 | 愛因斯坦大膽地預言，假若光子的頻率高於金屬的極限頻率，則這光子可以給予足夠能量來使得金屬表面的一個電子逃逸，造成光電效應。電子獲得的能量中，一部分被用來將金屬中的電子射出，這部分能量叫逸出功，（用 $E_{\mbox{w}}$ 表示），另一部分成為了逃逸電子的動能：
: $h\nu =E_{\mbox{w}}+{\frac {1}{2}}mv^{2}$
這裡 $m$ 是電子的質量， $v$ 是其速度。
假若光的頻率低於金屬的極限頻率，那麼它無法使得電子獲得足夠的逸出功。這時，不論輻照度有多大，照射時間有多長，都不會發生光電效應。而當入射光的頻率高於極限頻率時，即使光不夠強，當它射到金屬表面時也會觀察到光電子發射。羅伯特・密立根後來的實驗證明這些理論與預言屬實。
愛因斯坦將普朗克的量子理論加以延伸擴展，他提出不僅僅物質與電磁輻射之間的交互作用是量子化的，而且量子化是一個基本物理特性的理論。通過這個新理論，他得以解釋光電效應。
### 原子結構
20 世紀初，拉塞福模型被公認為正確的原子模型。這個模型假設帶負電荷的電子，像行星圍繞太陽運轉一樣，圍繞帶正電荷的原子核運轉。在這個過程中庫侖力與離心力必須平衡。
但是這個模型有兩個問題無法解決。首先，按照古典電磁學，這個模型不穩定，由於電子不斷地在它的運轉過程中被加速，它應該會通過發無線電磁波喪失能量，這樣它很快就會墜入原子核。其次，實驗結果顯示，原子的發射光譜是由一系列離散的發射線組成，比如氫原子的發射光譜是由一個紫外線系列（來曼系）、一個可見光系列（巴耳麥系）和其它的紅外線系列組成；而按照古典理論原子的發射譜應該是連續的。
1913 年，尼爾斯・波耳提出了波耳模型，這個模型引入量子化的概念來解釋原子結構和光譜線。波耳認為，電子只能在對應某些特定能量值 $E_{n}$ 的軌道上運動。假如一個電子，從一個能量比較高的軌道（ $E_{n}$ ），躍遷到一個能量比較低的軌道（ $E_{m}$ ）上時，它發射的光的頻率為
: $\nu ={\frac {E_{n}-E_{m}}{h}}$
反之，通過吸收同樣頻率的光子，電子可以從低能的軌道，躍遷到高能的軌道上。
波耳模型可以解釋氫原子的結構。改善的波耳模型，還可以解釋類氫原子的結構，即 He+, Li2+, Be3+ 等。但它還不夠完善，仍然無法準確地解釋其它原子的物理現象。
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量子物理学 | 1924 年，路易・德布羅意發表博士論文提出，粒子擁有波動性，其波長 $\lambda _{Broglie}$ 與動量 $p$ 成反比，以方程式表示為
: $\lambda _{Broglie}={\frac {h}{p}}$ 。
這理論稱為德布羅意假說，又稱為物質波假說。這意味著電子不但具有粒子性，還具有波動性。
1927 年，柯林頓・戴維森與雷斯特・革末做實驗將低能量電子入射於鎳晶體，然後測量對於每一個角度的散射強度。從分析實驗數據，他們發現，假設加速電位為 5.4eV，則在 50° 之處會出現強勁反射，符合威廉・布拉格於 1913 年所提出的 X 射線繞射性質。這驚人的結果證實電子是一種物質波，也證實了物質波假說。這實驗就是著名的戴維森－革末實驗。
電子的雙縫實驗可以非常生動地展示出多種不同的量子力學現象。如右圖所示，
* 打在屏幕上的電子是點狀的，這個現象與一般感受到的點狀的粒子相同。
* 電子打在屏幕上的位置，有一定的分布機率，隨時間可以看出雙縫繞射所特有的條紋圖像。假如一個光縫被關閉的話，所形成的圖像是單縫特有的波的分布機率。
在圖中的實驗裡，電子源的強度非常低，所發射出的電子與電子之間的距離約為 150km，任意兩個電子同時存在於電子發射器與探測屏之間的機率微乎其微。顯然可以推斷，單獨電子同時通過了兩條狹縫，自己與自己發生干涉，從而出現這個干涉圖樣。對於古典物理學來說，這個解釋非常奇怪。從量子力學的角度來看，電子的分布機率可以用兩個分別通過兩條狹縫的量子態疊加在一起來解釋。這個實驗非常具有信服力地展示出電子的波動性。
## 數學基礎
在二十世紀二十年代，出現了兩種量子物理的理論，即維爾納・海森堡的矩陣力學和埃爾溫・薛丁格的波動力學。 | [
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量子物理学 | 海森堡主張，只有在實驗裏能夠觀察到的物理量（可觀察量），才具有物理意義，才可以用理論描述其物理行為，例如，不能直接觀察到電子運動於原子裏的位置與週期。因此，他著重於研究電子躍遷時所發射光波的離散頻率和輻照度，這些是可觀察量。但是，他無法實際應用這點子於氫原子問題，因為這問題太過複雜，他只能改應用這點子於比較簡單，但也比較不實際的問題。經過一番努力，他計算出諧振子問題的能譜與零點能量，符合分子光譜學的結果。另外，在海森堡理論中，系統的哈密頓量是位置和動量的函數，但它們不再具有古典力學中的定義，而是由二階（代表著過程的初態和終態）傅立葉係數的矩陣給出。海森堡還發現，這些矩陣互不對易。這些論述後來發展成為矩陣力學。
從德布羅意論文的相對論性理論，薛丁格推導出一種波動方程式，稱為薛丁格方程式；用這方程式可以計算出氫原子的譜線，得到與波耳模型完全相同的答案。波動力學的基礎方程式就是薛丁格方程式
薛丁格率先於 1926 年證明了這兩種理論的等價性。稍後，卡爾・埃卡特和沃爾夫岡・包立也給出類似證明，約翰・馮・諾伊曼嚴格地證明了波動力學和矩陣力學的等價性。
### 基礎公設
整個量子力學的數學理論可以建立於五個基礎公設。這些公設不能被嚴格推導出來，而是從實驗結果仔細分析歸納總結而得到的。從這五個公設，可以推導出整個量子力學。假若量子力學的理論結果不符合實驗結果，則必須將這些基礎公設加以修改，直到沒有任何不符合之處。至今為止，量子力學已被實驗核對至極高準確度，還沒有找到任何與理論不符合的實驗結果，雖然有些理論很難直覺地用古典物理的概念來理解，例如，波粒二象性、量子糾纏等等。
1. 量子態公設：量子系統在任意時刻的狀態（量子態）可以由希爾伯特空間 ${\mathcal {H}}$ 中的態矢量 $|\psi \rangle $ 來設定，這態矢量完備地給出了這量子系統的所有資訊。這公設意味著量子系統遵守態疊加原理，假若 $|\psi _{1}\rangle $ 、 $|\psi _{2}\rangle $ 屬於希爾伯特空間 ${\mathcal {H}}$ ，則 $c_{1}|\psi _{1}\rangle +c_{2}|\psi _{2}\rangle $ 也屬於希爾伯特空間 ${\mathcal {H}}$ , $c_{1}$ 和 $c_{2}$ 皆為常數。 | [
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量子物理学 | 2. 時間演化公設： 態矢量為 $|\psi (t)\rangle $ 的量子系統，其動力學演化可以用薛丁格方程式表示， $i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle $ ；其中，哈密頓算符 ${\hat {H}}$ 對應於量子系統的總能量， $\hbar $ 是約化普朗克常數。根據薛丁格方程式，假設時間從 $t_{0}$ 流動到 $t$ ，則態向量從 $|\psi (t_{0})\rangle $ 演化到 $|\psi (t)\rangle $ ，這過程以方程式表示為 $|\psi (t)\rangle ={\hat {U}}(t,t_{0})|\psi (t_{0})\rangle $ ；其中， ${\hat {U}}(t,t_{0})=e^{-i{\hat {H}}(t-t_{0})/\hbar }$ 是時間演化算符。
3. 可觀察量公設：每個可觀察量 $A$ 都有其對應的厄米算符 ${\hat {A}}$ ，而算符 ${\hat {A}}$ 的所有本徵矢量共同組成一個完備基底。
4. 塌縮公設：對於量子系統測量某個可觀察量 $A$ ，這動作可以數學表示為將其對應的厄米算符 ${\hat {A}}$ 作用於量子系統的態矢量 $|\psi \rangle $ ，測量值只能為厄米算符 ${\hat {A}}$ 的本徵值。在測量後，假設測量值為 $a_{i}$ ，則量子系統的量子態立刻會塌縮為對應於本徵值 $a_{i}$ 的本徵態 $|e_{i}\rangle $ 。
5. 波恩公設：對於這測量，獲得本徵值 $a_{i}$ 的機率為量子態 $|\psi \rangle $ 處於本徵態 $|e_{i}\rangle $ 的機率幅的絕對值平方。
### 量子態與量子算符
量子態指的是量子系統的狀態，態向量可以用來抽象地表現量子態。採用狄拉克標記，態向量表示為括量 $\left\vert \psi \right\rangle $ ；其中，在符號內部的希臘字母 $\psi $ 可以是任何符號，字母，數字，或單字。例如，沿著磁場方向測量電子的自旋，得到的結果可以是上旋或是下旋，分別標記為 $\left\vert \uparrow \right\rangle $ 或 $\left\vert \downarrow \right\rangle $ 。 | [
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量子物理学 | 對量子態做操作定義，量子態可以從一系列製備程序來辨認，即這程序所製成的量子系統擁有這量子態。例如，使用斯特恩 - 革拉赫實驗儀器，設定磁場朝著 z - 軸方向，如右圖所示，可以將入射的銀原子束，依照自旋的 z - 分量分裂成兩道，一道為上旋，量子態為 $\left\vert \uparrow \right\rangle $ ，另一道為下旋，量子態為 $\left\vert \downarrow \right\rangle $ ，這樣，可以製備成量子態為 $\left\vert \uparrow \right\rangle $ 的銀原子束，或量子態為 $\left\vert \downarrow \right\rangle $ 的銀原子束。原本銀原子束的態向量可以按照態疊加原理表示為
: $\left\vert \psi \right\rangle =\alpha \left\vert \uparrow \right\rangle +\beta \left\vert \downarrow \right\rangle $ ；
其中， $\alpha $ 、 $\beta $ 是複值係數， $|\alpha |^{2}$ 、 $|\beta |^{2}$ 分別為入射銀原子束處於上旋、下旋的機率， $|\alpha |^{2}+|\beta |^{2}=1$ 。 | [
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量子物理学 | 在斯特恩 - 革拉赫實驗裏，可以透過測量而得到自旋的 z - 分量，這種物理量稱為可觀察量，透過做實驗測量可以得到其測值。每一個可觀察量都有一個對應的量子算符；將算符作用於量子態，會使得量子態線性變換成另一個量子態。假若變換前的量子態與變換後的量子態，除了乘法數值以外，兩個量子態相同，則稱此量子態為此算符的本徵態，稱此乘法數值為此算符的本徵值。可觀察量的算符也許會有很多本徵值與本徵態。根據統計詮釋，每一次測量所得到的測值只能是其中的一個本徵值，而且，測得這本徵值的機會呈機率性，量子系統的量子態也會改變為對應於本徵值的本徵態。例如，自旋的 z - 分量是個可觀察量 $S_{z}$ ，做實驗可以得到的測值為 $+\hbar /2$ 或 $-\hbar /2$ 。對應於可觀察量 $S_{z}$ 的量子算符 ${\hat {S}}_{z}$ 有兩個本徵值分別為 $+\hbar /2$ 、 $-\hbar /2$ 的本徵態 $\left\vert \uparrow \right\rangle $ 、 $\left\vert \downarrow \right\rangle $ ，所以將量子算符 ${\hat {S}}_{z}$ 分別作用於這兩個本徵態，會得到
: ${\hat {S}}_{z}\left\vert \uparrow \right\rangle =+{\tfrac {\hbar }{2}}\left\vert \uparrow \right\rangle $ 、
: ${\hat {S}}_{z}\left\vert \downarrow \right\rangle =-{\tfrac {\hbar }{2}}\left\vert \downarrow \right\rangle $ 。 | [
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量子物理学 | 將量子算符 ${\hat {S}}_{z}$ 作用於量子態 $\left\vert \psi \right\rangle =\alpha \left\vert \uparrow \right\rangle +\beta \left\vert \downarrow \right\rangle $ ，會得到本徵值 $+\hbar /2$ 、 $-\hbar /2$ 的機率分別為 $|\alpha |^{2}$ 、 $|\beta |^{2}$ 。假若本徵值為 $+\hbar /2$ ，則量子態 $\left\vert \psi \right\rangle $ 會塌縮為量子態 $\left\vert \uparrow \right\rangle $ ；假若本徵值為 $-\hbar /2$ ，則量子態 $\left\vert \psi \right\rangle $ 會塌縮為量子態 $\left\vert \downarrow \right\rangle $ 。
### 動力學演化
在量子力學公設裏，第二項直接提到量子系統的動力學演化，其遵守含時薛丁格方程式，因此，量子態的演化在任意時刻可以被完全預測，具有連續性、命定性與可逆性。第四項提到，當對於量子系統作測量時，其量子態會塌縮至幾個本徵態中的一個本徵態，具有不連續性、機率性與不可逆性。怎樣調和這兩種不同的行為，一種是關於量子態的自然演化，另一種是關於測量引發的演化，這仍舊是未解決的物理學問題。
量子系統的動力學演化可以用不同的繪景來表現。通過重新定義，這些不同的繪景可以互相變換，它們實際上是等價的。假若要專注分析量子態怎樣隨著時間的流易而演化，時間演化算符怎樣影響量子態，則可採用薛丁格繪景。假若要專注了解對應於可觀察量的算符怎樣隨著時間的流易而演化、時間演化算符怎樣影響這些算符，則可採用海森堡繪景。
## 主要論題
### 測量過程
量子力學與古典力學的一個主要區別，在於怎樣理論論述測量過程。在古典力學裏，一個物理系統的位置和動量，可以同時被無限精確地確定和預測。在理論上，測量過程對物理系統本身，並不會造成任何影響，並可以無限精確地進行。在量子力學中則不然，測量過程本身會對系統造成影響。 | [
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量子物理学 | 怎樣才能正確地理論描述對於一個可觀察量的測量？設定一個量子系統的量子態，首先，將量子態分解為該可觀察量的一組本徵態的線性組合。測量過程可以視為對於本徵態的一個投影，測量結果是被投影的本徵態的本徵值。假設，按照某種程序製備出一個系綜，在這系綜裏，每一個量子態都與這量子態相同，現在對於這系綜裏的每一個量子態都進行一次測量，則可以獲得所有可能的測量值（本徵值）的機率分布，每個測量值的機率等於量子態處於對應的本徵態的機率幅的絕對值平方。
因此，假設對於兩個不同的可觀察量 $A$ 和 $B$ 做測量，改變測量順序，例如從 $AB$ 改變為 $BA$ ，則可能直接影響測量結果。假若測量結果有所不同，則稱這兩個可觀察量為不相容可觀察量；否則，稱這兩個可觀察量為相容可觀察量。以數學術語表達，兩個不相容可觀察量 $A$ 和 $B$ 的對易算符不等於零：
: $[{\hat {A}},{\hat {B}}]\ {\stackrel {def}{=}}\ {\hat {A}}{\hat {B}}-{\hat {B}}{\hat {A}}\neq 0$ 。
### 不確定性原理
不確定性原理表明，越能準確地設定粒子的位置，則越不能準確地設定粒子的動量，反之亦然，以方程式表示為
: $\Delta x\Delta p\geq {\frac {\hbar }{2}}$ ；
其中， $\Delta x$ 、 $\Delta p$ 分別為位置、動量的不確定性。
設想一個定域性的波包，假設波包的尺寸為 $L$ ．從計數波包的週期數 $N$ ，可以知道其波數 $k$ ：
: $k=2\pi N/L$ 。
假若，計數 $N$ 的不確定性為 $\Delta N=1$ ，那麼，波數的不確定性是
: $\Delta k=2\pi /L$ 。
根據德布羅意假說， $P=\hbar k$ 。因此，動量的不確定性是
: $\Delta P=\hbar \Delta k={\frac {h}{L}}$ 。
由於粒子位置的不確定性是 $\Delta X\approx L/2$ ，所以，這兩個不相容可觀察量的不確定性為
: $\Delta P\Delta X\approx h/2$ 。
### 全同粒子 | [
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量子物理学 | 粒子具有很多種物理性質，例如質量、電荷、自旋等等。假若兩個粒子具有不同的性質，則可以藉著測量這些不同的性質來區分這兩個粒子。根據許多實驗獲得的結果，同種類的粒子具有完全相同的性質，例如，宇宙裏所有的電子都帶有相等數量的電荷。因此，無法依靠物理性質來區分同種類的粒子，必須使用另一種區分法，即跟蹤每一個粒子的軌道。只要能夠無限精確地測量出每一個粒子的位置，就不會搞不清楚哪一個粒子在哪裡。這個適用於古典力學的方法有一個問題，那就是它與量子力學的基本原理相矛盾。根據量子理論，在位置測量期間，粒子並不會保持明確的位置。粒子的位置具有機率性。隨著時間的流易，幾個粒子的量子態可能會移動蔓延，因此某些部分會互相重疊在一起。假若發生重疊事件，給每個粒子「掛上一個標籤」的方法立刻就失去了意義，就無法區分在重疊區域的兩個粒子。
全同粒子所呈現出的不可區分性，對量子態的對稱性，以及多粒子系統的統計力學，有深遠的影響。比如說，一個由全同粒子組成的多粒子系統量子態，在交換兩個粒子「1」和粒子「2」時，可以證明，不是對稱的 $(|\psi _{12}\rangle =+|\psi _{21}\rangle )$ ，就是反對稱的 $(|\psi _{12}\rangle =-|\psi _{21}\rangle )$ 。具有對稱性的粒子被稱為玻色子，具有反對稱性的粒子被稱為費米子。此外自旋的對換也形成對稱：自旋為半數的粒子（如電子、質子和中子）是反對稱的，因此是費米子；自旋為整數的粒子（如光子）是對稱的，因此是玻色子。
由於費米子系統具有反對稱性，費米子遵守包立不相容原理，即兩個費米子無法占據同一狀態。這個原理擁有極大的實用意義。它表明，在由原子組成的物質世界裡，電子無法同時占據同一狀態，因此在最低狀態被占據後，下一個電子必須占據次低的狀態，直到所有的狀態均被滿足為止。這個現象決定了物質的物理和化學特性。
費米子與玻色子的狀態的熱分布也相差很大：玻色子遵循玻色 - 愛因斯坦統計，而費米子則遵循費米 - 狄拉克統計。
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量子物理学 | 假設兩個粒子在經過短暫時間彼此耦合之後，單獨攪擾其中任意一個粒子，儘管兩個粒子之間可能相隔很長一段距離，還是會不可避免地影響到另外一個粒子的性質，這種關聯現象稱為量子糾纏。往往由多個粒子組成的量子系統，其狀態無法被分離為其組成的單個粒子的狀態，在這種情況下，單個粒子的狀態被稱為是纏結的。纏結的粒子有驚人的特性，這些特性違背一般的直覺。比如說，對一個粒子的測量，可以導致整個系統的波包立刻塌縮，因此也影響到另一個、遙遠的、與被測量的粒子纏結的粒子。這個現象並不違背狹義相對論，因為在量子力學的層面上，在測量粒子前，它們不能被單獨各自定義，實際上它們仍是一個整體。不過在測量它們之後，它們就會脫離量子纏結的狀態。
### 量子去相干
作為一個基本理論，量子力學原則上，應該適用於任何大小的物理系統，也就是說不僅限於微觀系統，那麼，它應該提供一個過渡到宏觀古典物理的方法。量子現象的存在提出了一個問題，即怎樣從量子力學的觀點，解釋宏觀系統的古典現象。尤其無法直接看出的是，量子力學中的量子疊加，在宏觀世界怎樣呈現出來。1954 年，愛因斯坦在給馬克斯・玻恩的信中，就提出了怎樣從量子力學的角度，來解釋宏觀世界的物理現象的問題，他指出僅僅量子力學現象太「小」無法解釋這個問題。這個問題的另一個例子是由薛丁格提出的薛丁格貓的思想實驗。
後來，物理學者領會到，上述的思想實驗，實際而言並不合乎現實，因為它們忽略了不可避免地與周圍環境的交互作用，量子系統會因為這交互作用與環境關聯在一起。處於疊加態的量子系統非常容易受周圍環境的影響，而且隨著時間流逝，這量子系統會與環境永無休止地越加深入糾纏，這現象稱為「馮紐曼無窮鏈」（Von Neumann's infinite chain）。在疊加態裏，幾個相互正交的量子態疊加在一起，彼此相干。量子去相干是一種過程，能夠將量子系統的約化密度矩陣對角化，而相干性質就是表示於這約化密度矩陣的非對角元素，所以，疊加態的相干性質會快速消失，無法再被探測到，從而呈現出古典的統計性質。雖然量子系統的疊加態不再具有相干性質，整個量子系統與環境共同組成的聯合態仍舊具有相干性質。
對於量子計算機來說，量子去相干也有實際意義。在一台量子計算機中，需要多個量子狀態儘可能地長時間保持疊加。去相干時間短是一個非常大的技術問題，因為它會削弱量子疊加效應，但它也是一個必需的因素，因為儲存在計算機內的數據必需經過量子測量被讀出來。
## 與其它物理理論的關係
### 古典物理 | [
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量子物理学 | 量子力學的預測已被實驗核對至極高準確度，是在科學領域中，最為準確的理論之一。對應原理實現古典力學與量子力學之間的對應關係，根據對應原理，假若量子系統已達到某「古典極限」，則其物理行為可以很精確地用古典理論來描述；這古典極限可以是大量子數極限，也可以是普朗克常數趨零極限。實際而言，許多宏觀系統都是用古典理論（如古典力學和電磁學）來做精確描述。因此在非常「大」的系統中，量子力學的特性應該會逐漸與古典物理的特性相近似，兩者必須相互符合。
對應原理對於建立一個有效的量子力學模型是很重要的輔助工具。量子力學的數學基礎相當廣泛寬鬆，它僅只要求量子系統的態向量屬於希爾伯特空間，其可觀察量是線性的厄米算符，它並沒有規定在實際情況下，應該選擇哪一種希爾伯特空間、哪些厄米算符。因此，在實際情況下，必須選擇相應的希爾伯特空間和算符來描寫一個特定的量子系統。而對應原理則是做出這個選擇的一個重要輔助工具。這個原理要求量子力學所做出的預言，在越來越大的系統中，逐漸近似古典理論的預言。這個大系統的極限，被稱為「古典極限」或者「對應極限」。因此可以使用啟發法的手段，來建立一個量子力學的模型，而這個模型的極限，就是相應的古典物理學的模型。
在古典系統與量子系統之間，量子相干是一種很明顯可以用來區分的性質，具有量子相干性的電子、光子等等微觀粒子可以處於量子疊加態，不具有量子相干性的棒球、老虎等等宏觀系統不可以處於量子疊加態。量子去相干可以用來解釋這些行為。一種應用這性質來區分的工具是貝爾不等式，遭到量子糾纏的系統不遵守貝爾不等式，而量子去相干能夠將量子糾纏性質變換為古典統計性質，系統的物理行為因此可以用隱變數理論解釋，不再不遵守貝爾不等式。簡略而言，量子干涉是將幾個量子態的量子幅總和在一起，而古典干涉則是將幾個古典波動的波強總和在一起。對於微觀物體，整個系統的延伸尺寸超小於相干長度，因此會產生長程量子糾纏與其它非定域現象，一些量子系統的特徵行為。通常，量子相干不會出現於宏觀系統。
### 狹義相對論
原本量子力學的表述所針對的模型，其對應極限為非相對論性古典力學。例如，眾所皆知的量子諧振子模型使用了非相對論性表達式來表達其動能，因此，這模型是古典諧振子的量子版本。 | [
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量子物理学 | 早期，對於合併量子力學與狹義相對論的試圖，涉及到使用協變方程式，例如，克萊因 - 戈爾登方程式或狄拉克方程式，來取代薛丁格方程式。這些方程式雖然能夠很成功地描述許多量子現象，但它們目有某些不滿意的問題，它們無法描述在相對論性狀況下，粒子的生成和湮滅。完整的相對論性量子理論需要量子場論的關鍵發展。量子場論能夠將場量子化（而不是一組固定數量的粒子）。第一個量子場論是量子電動力學，它可以精確地描寫電磁交互作用。量子電動力學其對於某些原子性質的理論預測，已被證實準確至 108 分之一。
對於描述電磁系統，時常不需要使用到量子場論的全部功能。比較簡單的方法，是將帶電粒子當作處於古典電磁場中的量子力學物體。這個手段從量子力學的初期，就已經被使用了。比如說，氫原子的電子狀態，可以近似地使用古典的 $1/r$ 庫侖勢來計算。這就是所謂的半古典方法。但是，在電磁場中的量子起伏起一個重要作用的情況下（比如帶電粒子發射一顆光子）這個近似方法就失效了。
### 粒子物理學
專門描述強交互作用、弱交互作用的量子場論已發展成功。強交互作用的量子場論稱為量子色動力學，這個理論描述次原子粒子，例如夸克、膠子，它們彼此之間的交互作用。弱交互作用與電磁交互作用也被統一為單獨量子場論，稱為電弱交互作用。
### 廣義相對論
量子引力是對引力場進行量子化描述的理論，屬於萬有理論之一。物理學者發覺，建造引力的量子模型是一件非常艱難的研究。半古典近似是一種可行方法，推導出一些很有意思的預測，例如，霍金輻射等等。可是，由於廣義相對論（至今為止，最成功的引力理論）與量子力學的一些基礎假說相互矛盾，表述出一個完整的量子引力理論遭到了嚴峻阻礙。嘗試結合廣義相對論與量子力學是熱門研究方向，為當前的物理學尚未解決的問題。當前主流嘗試理論有：超弦理論、迴圈量子重力理論等等。
## 哲學觀點
量子力學是經歷最嚴格驗證的物理理論之一。至今為止，尚未找到任何能夠推翻量子力學的實驗數據。大多數物理學者認為，「幾乎」在所有情況下，它正確地描寫能量和物質的物理性質。雖然如此，量子力學中，依然存在著概念上的弱點和缺陷，除前面所述關於萬有引力的量子理論的缺乏以外，現今，對於量子力學的詮釋依然存在著嚴重爭議。 | [
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量子物理学 | 從初始到現今，量子力學的各種反直覺論述與結果一直不停地引起在哲學、詮釋方面的強烈辯論。甚至一些基礎論點，例如，馬克斯・玻恩關於機率幅與機率分佈的基本定則，也需要經過數十年的嚴格思考論證，才被學術界接受。理察・費曼曾經說過一句銘言：「我認為我可以有把握地說，沒有人懂得量子力學！」史蒂文・溫伯格承認：「依照我現在的看法，完全令人滿意的量子力學詮釋並不存在。」
雖然在發表後已經過七十幾年光陰，哥本哈根詮釋仍舊是最為物理學者接受的對於量子力學的一種詮釋。它的主要貢獻者是尼爾斯・波耳與沃納・海森堡。根據這種詮釋，量子力學的機率性論述不是一種暫時補丁，並且最終將會被一種命定性理論取代，它必須被視為一種最終拋棄古典因果論思維的動作。在這裡，任何量子力學形式論的良好定義的應用必須將實驗設置納入考量，這是因為不同實驗狀況獲得的結果所具有的互補性。
身為量子理論的創始者之一的愛因斯坦很不滿意這種非命定性的論述。他認為量子力學不具有完備性，他提出一系列反駁論述，其中最著名的就是愛因斯坦 - 波多爾斯基 - 羅森佯謬。這佯謬建立於定域實在論。假設局區域實在論成立，則量子力學不具有完備性。接近三十年以後，約翰・貝爾發佈論文表示，對於這個佯謬稍加理論延伸，就會導致對於量子力學與定域實在論出現不同的預言，因此可以做實驗檢試量子世界到底與哪種預言一致。為此，完成了很多相關實驗，這些實驗確定量子力學的預言正確無誤，定域實在論無法描述量子世界。
休・艾弗雷特三世提出的多世界詮釋認為，量子理論所做出的可能性的預言，全部會同步實現，這些現實成為彼此之間毫無關聯的平行宇宙。在這種詮釋裏，波函數不塌縮，它的發展是決定性的。但是由於隻身觀察者無法存在於所有的平行宇宙裏，只能觀察在身處的宇宙內發生的事件，而無法觀察到其它平行宇宙內發生的事件。這種詮釋不需要特殊處理測量動作。在這理論裏，薛丁格方程式無論何處無論何時都成立。對於任何測量動作，必須將整個系統，測量儀器與被測量物體，全部納入薛丁格方程式的運算。測量儀器與被測量物體所有可能的量子態都存在於一種真實的量子疊加，形成了糾纏態。雖然平行宇宙具有命定性，觀察者意識到由機率主導的非命定行為，因為觀察者只能觀察到自身所在的宇宙。多世界詮釋能夠透過貝爾的檢試實驗。近期研究發展將多世界詮釋與量子去相干理論合併在一起來解釋主觀的波函數塌縮。由於量子去相干機制，糾纏態會快速地演化為古典混合態。 | [
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量子物理学 | 戴維・玻姆提出了一種非定域性的隱變量理論，稱為導航波理論。在這種詮釋裏，波函數被理解為粒子的一個導航波。從結果上，這個理論預言的實驗結果，與非相對論哥本哈根詮釋的預言完全一樣，因此，使用實驗手段無法鑑別這兩個解釋。雖然這個理論的預言是命定性的，但是由於不確定原理無法推測出隱變量的精確狀態，其結果跟哥本哈根詮釋的結果一樣，使用導航波理論來解釋，實驗的結果具有機率性。至今為止，還不能確定這個解釋是否能夠擴展到相對論量子力學上去。路易・德布羅意和其他人也提出過類似的隱變量解釋。
## 應用
在許多現代技術裝備中，量子效應起了重要的作用，例如，雷射的工作機制是愛因斯坦提出的受激發射、電子顯微鏡利用電子的波粒二象性來增加解析度、原子鐘使用束縛於原子的電子從一個能級躍遷至另一個能級時所發射出的微波信號的頻率來計算與維持時間的準確性、核磁共振成像倚賴核磁共振機制來探測物體內部的結構。對半導體的研究導致了二極體和三極體的發明，這些都是現代電子系統與電子器件不可或缺的元件。
以下列出了一些量子力學的應用，但實際上其應用並不限於這些領域。
### 電子器件
量子力學在電子器件中得到了廣泛應用。比如發光二極體在日常照明中應用中越來越廣泛。現代計算機的基礎，微處理器，由上億個半導體電晶體集成，且隨著電晶體數量的增加，電晶體中的量子效應越來越明顯。量子力學對於解釋和模擬半導體器件中的電學、光學、熱學性質等尤其重要。
量子力學還是量子穿隧器件工作的基礎。比如 USB 非易失性快閃記憶體中，資訊的存儲和讀取都通過量子穿隧實現。
超導電子器件也與量子力學有著密切的關係。
### 計算機
相比於電晶體等電子器件，量子計算機的研製則更為前沿。在一些特定算法下，量子計算機的速度會比古典架構的計算機快成千上萬倍（比如量子退火算法）。古典計算機使用 0 和 1 作為比特，而量子計算機則使用量子位作為基本單位。量子位由不同的電子態疊加形成。
### 宇宙學
量子力學能夠用來解釋很多奇異的宇宙現象，例如，宇宙微波背景的頻譜可以用普朗克黑體輻射定律來解釋。宇宙微波背景證實了大爆炸理論的正確無誤，自此，穩態理論開始式微。從宇宙微波背景可以推論，早期宇宙非常炙熱、對於電磁輻射不透明、具有均質性與各向同性，是標準的黑體。 | [
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Subsets and Splits