Heisenberg group by 90°. The other reflections are "xyx" and "yxy", and rotation by 180° is "xyxy" (="yxyx"). The Lie algebra formula_16 of the Heisenberg group formula_1 (over the real numbers) is the space of formula_18 matrices of the form with formula_20. The following three elements form a basis for formula_16: The basis elements satisfy the commutation relations: The name "Heisenberg group" is motivated by the preceding relations, which have the same form as the canonical commutation relations in quantum mechanics: where formula_25 is the position operator, formula_26 is the momentum operator, and formula_27 is Planck's constant. The Heisenberg group formula_1 has
Werner Heisenberg and the whole"). Heisenberg died of cancer of the kidneys and gallbladder at his home, on 1 February 1976. The next evening, his colleagues and friends walked in remembrance from the Institute of Physics to his home and each put a candle near the front door. He is buried at Munich Waldfriedhof. Heisenberg was awarded a number of honors: The following reports were published in "Kernphysikalische Forschungsberichte" ("Research Reports in Nuclear Physics"), an internal publication of the German "Uranverein". The reports were classified Top Secret, they had very limited distribution, and the authors were not allowed to keep copies. The