what is Bloch theorem
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Bloch theorem Bloch theorem. A theorem that specifies the form of the wave functions that characterize electron energy levels in a periodic crystal. Electrons that move in a constant potential, that is, a potential independent of the position r, have wave functions that are plane waves, having the form exp(i k · r).he theorem that the lowest state of a quantum-mechanical system without a magnetic field can carry no current. (solid-state physics). The theorem that, in a periodic structure, every electronic wave function can be represented by a Bloch function.
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Chebyshev's Theorem But for k ³ 1, Chebyshev's Theorem provides a lower bound to the proportion of measurements that are within a certain number of standard deviations from the mean. This lower bound estimate can be very helpful when the distribution of a particular population is unknown or mathematically intractable.
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Ore's theorem Ore's theorem. For Ore's theorem in ring theory, see Ore condition. Ore's theorem is a result in graph theory proved in 1960 by Norwegian mathematician Øystein Ore. It gives a sufficient condition for a graph to be Hamiltonian, essentially stating that a graph with sufficiently many edges must contain a Hamilton cycle.
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- The Pythagorean theorem may be the best-known equation in mathematics. Its origins reach back to the beginnings of civilization, and today every student continues to study it. What most nonmathematicians don't understand or appreciate is why this simply stated theorem has fascinated countless generations.
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- The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students. The Pythagorean Theorem is Pythagoras' most famous mathematical contribution.
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Bohr model The Bohr model is a relatively primitive model of the hydrogen atom, compared to the valence shell atom. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics and thus may be considered to be an obsolete scientific theory.
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- In this illustration, line EB is parallel to side CD. (We can see that it intersects sides AC and AD .) This creates proportional segments: In fact, we even have a theorem about this: the Triangle Proportionality Theorem. Apparently, mathematicians got quite a giggle when they first came up with it, as it has earned the nickname of The Side-Splitter Theorem. (To be honest, we don't really get it.
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How to Prove the Pythagorean Theorem The theorem states that the sum of the squares of the two sides of a right triangle equals the square of the hypotenuse: a2 + b2 = c2. The theorem can be proved in many different ways involving the use of squares, triangles, and geometric concepts. Two common proofs are presented here.
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Chebyshev's Theorem Chebyshev's Theorem. The Russian mathematician P. L. Chebyshev (1821- 1894) discovered that the fraction of observations falling between two distinct values, whose differences from the mean have the same absolute value, is related to the variance of the population.
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Hess's law Hess's law. Hess's law of constant heat summation, also known as Hess's law (or Hess' law), is a relationship in physical chemistry named after Germain Hess, a Swiss-born Russian chemist and physician who published it in 1840.
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- (pĭ-thāg'ə-rē'ən) A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.
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- In fact, without the concept of the square root, not even the Pythagorean theorem can be fully grasped. Pythagorean theorem. A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides. It is mathematically stated as c2 = a2 + b2, where c is the length of the hypotenuse and a and b the lengths of the other two sides. The theorem in geometry that, in a triangle with one right angle, usually called a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
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Atomic packing factor In crystallography, atomic packing factor (APF), packing efficiency or packing fraction is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. In atomic systems, by convention, the APF is determined by assuming that atoms are rigid spheres.
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Equipartition theorem In 1811, Italian physicist and mathematician Amedeo Avogadro published a hypothesis (also termed Avogadro's law or principle) stating that the volume of a gas is directly proportional to the number of molecules of the gas. where a is a constant, V is the volume of the gas, and N is the number of gas molecules.
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Bernoulli's principle Bernoulli's principle, An increase in the velocity of a fluid that is accompanied by a decrease of pressure. Swiss scientist, Daniel Bernoulli (1700-1782), demonstrated that, in most cases, the pressure in a liquid or gas decreases as the liquid or gas moves faster. This explains in part why a wing lifts an airplane.
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Pascal's principle Pascal’s law (also known as Pascal’s principle) is the statement that in a fluid at rest in a closed container, a pressure change in one part is transmitted without loss to every portion of the fluid and to the walls of the container.
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Bohr model Not only did the Bohr model explain the reason for the structure of the Rydberg formula, it also provided a justification for its empirical results in terms of fundamental physical constants. The Bohr model is a relatively primitive model of the hydrogen atom, compared to the valence shell atom. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics and thus may be considered to be an obsolete scientific theory.
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- Pythagorean theorem is used to find the lengths, distances and heights using right triangles which model real life situations. When fire occurs in high raise buildings, the fire fighting men cannot use the regular stairs or lifts.
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Pythagoras: Facts and Information He is best known for the Pythagorean theory named after him. Often referred to as Pythagoras’ Rule, Pythagoras’ Theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. He believed that science and religion were connected.
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- 1 Lecture Note on Solid State Physics Bloch theorem and Energy band Masatsugu Suzuki and Itsuko S. Suzuki Department of Physics, State University of New York at Binghamton, Binghamton, New York 13902-6000 (May 9, 2006) Abstract Here we consider a wavefunction of an electron in a periodic potential of metal. Lecture Note on Solid State Physics Bloch theorem and Energy band Masatsugu Suzuki and Itsuko S. Suzuki Department of Physics, State University of New York at Binghamton, Binghamton, New York 13902-6000 (May 9, 2006) Abstract Here we consider a wavefunction of an electron in a periodic potential of metal.
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Zaitsev's rule Zaitsev's rule (or Saytseff's rule, Saytzev rule) is an empirical rule for predicting the favored alkene product(s) in elimination reactions. While at the University of Kazan, Russian chemist Alexander Zaitsev studied a variety of different elimination reactions and observed a general trend in the resulting alkenes.or example, when 2-iodobutane is treated with alcoholic KOH, 2-butene is the major product and 1-butene is the minor product. More generally, Zaitsev's rule predicts that in an elimination reaction, the most stable alkene – typically the most substituted one – will be the favored product.
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- Fundamental theorem of arithmetic. From Wikipedia, the free encyclopedia. The Fundamental theorem of arithmethic (also called the unique factorization theorem) is a theorem of number theory. The theorem says that every positive integer greater than 1 can be written as a product of prime numbers (or the integer is itself a prime number).
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Gauss's law In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. The surface under consideration may be a closed one enclosing a volume such as a spherical surface. The law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1813, both in the context of the attraction of ellipsoids. It is one of Maxwell's four equations, which form the basis of classical electrodynamics. Gaus
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- The Triangle Proportionality Theorem says that, if a line is parallel to one side of a triangle, then it splits the other two sides into proportional sections. We can use this theorem to find the value of x in ∆ ACE. We're given that line BD is parallel to side AE, and three of the resulting segment lengths are also given. To find the missing piece, set up a proportion comparing the side lengths: 16 ⁄ 4 = 12 ⁄ x.
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- Pythagorean Theorem Definition. In a right triangle the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. then the hypotenuse is the side opposite to the right angle (AB) and the legs (BC and CA) are the sides containing the right angle. a2 + b2 = c2.
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Surprising Uses of the Pythagorean Theorem Useful Application: Conservation of Squares. The Pythagorean Theorem applies to any equation that has a square. The triangle-splitting means you can split any amount (c2) into two smaller amounts (a2 + b2) based on the sides of a right triangle. In reality, the length of a side can be distance, energy, work, time, or even people in a social network: