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 bracket. This Lie algebra is a one-dimensional central extension of the commutative Lie algebra formula_57, isomorphic to the Lie algebra of the Heisenberg group. The general abstraction of a Heisenberg group is constructed from any symplectic vector space. For example, let ("V",ω) be a finite-dimensional real symplectic vector space (so ω is a nondegenerate skew symmetric bilinear form on "V"). The Heisenberg group H("V") on ("V",ω) (or simply "V" for brevity) is the set "V"×R endowed with the group law The Heisenberg group is a central extension of the additive group "V". Thus there is an exact sequence Any symplectic