Heisenberg picture Heisenberg picture In physics, the Heisenberg picture (also called the Heisenberg representation) is a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which the operators (observables and others) incorporate a dependency on time, but the state vectors are time-independent, an arbitrary fixed basis rigidly underlying the theory. It stands in contrast to the Schrödinger picture in which the operators are constant, instead, and the states evolve in time. The two pictures only differ by a basis change with respect to time-dependency, which corresponds to the difference between active and passive transformations. The Heisenberg picture is the
Heisenberg group case is the theta representation of the Heisenberg group, of which the discrete case gives the theta function. The Heisenberg group also occurs in Fourier analysis, where it is used in some formulations of the Stone–von Neumann theorem. In this case, the Heisenberg group can be understood to act on the space of square integrable functions; the result is a representation of the Heisenberg groups sometimes called the Weyl representation. The three-dimensional Heisenberg group "H"(R) on the reals can also be understood to be a smooth manifold, and specifically, a simple example of a sub-Riemannian manifold. Given a point "p"=("x","y","z")