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 connection with the theta functions. If , are integers (in the ring Z) then one has the discrete Heisenberg group H(Z). It is a non-abelian nilpotent group. It has two generators, and relations where is the generator of the center of H. (Note that the inverses of "x", "y", and "z" replace the 1 above the diagonal with −1.) By Bass's theorem, it has a polynomial growth rate of order 4. One can generate any element through If one takes "a, b, c" in Z/"p" Z for an odd prime "p", then one has the Heisenberg group modulo p. It