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
Jochen Heisenberg Jochen Heisenberg Jochen Heisenberg (born 16 May 1939) is a German physicist specializing in nuclear physics, and Professor Emeritus of Physics at the University of New Hampshire. He is the son of Nobel Prize-winning physicist Werner Heisenberg, who is best known for the uncertainty principle. He is the brother of German neurobiologist and geneticist Martin Heisenberg and the uncle of film director Benjamin Heisenberg. Heisenberg studied physics with Willibald Jentschke at the University of Hamburg and received his PhD in 1968. He then spent a two-year postdoctoral fellowship at Stanford University. From 1970-1978 he was a member of the faculty