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 priority over the historically applied concept of scholarly ability, even though its two most prominent supporters were the Nobel Laureates in Physics Philipp Lenard and Johannes Stark. There had been many failed attempts to have Heisenberg appointed as professor at a variety of German universities. His attempt to be appointed as the successor to Arnold Sommerfeld failed because of opposition by the "Deutsche Physik" movement. On 1 April 1935, the eminent theoretical physicist Sommerfeld, Heisenberg's doctoral advisor at the Ludwig-Maximilians-Universität München, achieved emeritus status. However, Sommerfeld stayed in his chair during the selection process for his successor, which took until