Werner Heisenberg mechanics formulation of quantum mechanics. On 1 May 1926, Heisenberg began his appointment as a university lecturer and assistant to Bohr in Copenhagen. It was in Copenhagen, in 1927, that Heisenberg developed his uncertainty principle, while working on the mathematical foundations of quantum mechanics. On 23 February, Heisenberg wrote a letter to fellow physicist Wolfgang Pauli, in which he first described his new principle. In his paper on the principle, Heisenberg used the word ""Ungenauigkeit"" (imprecision), not uncertainty, to describe it. In 1927, Heisenberg was appointed "ordentlicher Professor" (professor ordinarius) of theoretical physics and head of the department of physics
Heisenberg group operators on formula_103: for formula_109. So too do the multiplications by characters: for formula_111. These operators do not commute, and instead satisfy multiplication by a fixed unit modulus complex number. So the Heisenberg group formula_113 associated with "K" is a type of central extension of formula_114, via an exact sequence of groups: More general Heisenberg groups are described by 2-cocyles in the cohomology group formula_116. The existence of a duality between formula_117 and formula_101 gives rise to a canonical cocycle, but there are generally others. The Heisenberg group acts irreducibly on formula_103. Indeed, the continuous characters separate points so any