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
Max Planck Institute for Physics first head director. In October 1922, Max von Laue succeeded Einstein as managing director. Einstein gave up his position as a director of the institute in April 1933. The Institute took part in the German nuclear weapon project from 1939-1942. A year after the end of fighting in Europe in World War II, the institute was moved to Göttingen and renamed the Max Planck Institute for Physics, with Heisenberg continuing as managing director. In 1946, Carl Friedrich von Weizsäcker and Karl Wirtz joined the faculty as the directors for theoretical and experimental physics, respectively. In June 1942, Werner Heisenberg took