Heisenberg group of the Heisenberg group is fairly simple – later generalized by Mackey theory – and was the motivation for its introduction in quantum physics, as discussed below. For each nonzero real number formula_27, we can define an irreducible unitary representation formula_48 of formula_31 acting on the Hilbert space formula_50 by the formula: This representation is known as the Schrödinger representation. The motivation for the this representation is the action of the exponentiated position and momentum operators in quantum mechanics. The parameter formula_52 describes translations in position space, the parameter formula_53 describes translations in momentum space, and the parameter formula_54 gives
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