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 at the University of Würzburg and Jochen a physics professor at the University of New Hampshire. Heisenberg enjoyed classical music and was an accomplished pianist. Heisenberg was raised and lived as a Lutheran Christian. His autobiography starts with the young Heisenberg in his late teenage years, reading Plato's "Timaeus" while hiking in the Bavarian Alps. Heisenberg recounted the philosophical conversations with his fellow students and teachers on understanding the atom while receiving his scientific training in Munich, Göttingen and Copenhagen. In his speech Scientific and Religious Truth (1974) while accepting the Romano Guardini Prize, Heisenberg affirmed: In his late-sixties Heisenberg