Heisenberg picture once more and solving for them with proper initial conditions, leads to Direct computation yields the more general commutator relations, For formula_26, one simply recovers the standard canonical commutation relations valid in all pictures. For a time-independent Hamiltonian "H", 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
Heisenberg group group of a locally compact abelian group "K", equipped with a Haar measure. Such a group has a Pontrjagin dual formula_101, consisting of all continuous formula_102-valued characters on "K", which is also a locally compact abelian group if endowed with the compact-open topology. The Heisenberg group associated with the locally compact abelian group "K" is the subgroup of the unitary group of formula_103 generated by translations from "K" and multiplications by elements of formula_101. In more detail, the Hilbert space formula_103 consists of square-integrable complex-valued functions formula_106 on "K". The translations in "K" form a unitary representation of "K" as