Heisenberg picture formulation of matrix mechanics in an arbitrary basis, in which the Hamiltonian is not necessarily diagonal. It further serves to define a third, hybrid, picture, the interaction picture. In the Heisenberg picture of quantum mechanics the state vectors, |"ψ("t")"〉, do not change with time, while observables satisfy where is the Hamiltonian and <nowiki>[•,•]</nowiki> denotes the commutator of two operators (in this case and ). Taking expectation values automatically yields the Ehrenfest theorem, featured in the correspondence principle. By the Stone–von Neumann theorem, the Heisenberg picture and the Schrödinger picture are unitarily equivalent, just a basis change in Hilbert space. In
Werner Heisenberg in physics—Heisenberg had participated in the doctoral examination of one of them at the Universität Leipzig. The most influential of the three was Johannes Juilfs. During their investigation, they became supporters of Heisenberg as well as his position against the ideological policies of the "Deutsche Physik" movement in theoretical physics and academia. On 29 June 1936, a Nazi Party newspaper published a column attacking Heisenberg. On 15 July 1937, he was attacked in a journal of the SS. In mid-1936, Heisenberg presented his theory of cosmic-ray showers in two papers. Four more papers appeared in the next two years. In