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 the special property that the exponential map is a one-to-one and onto map from the Lie algebra formula_16 to the group formula_1. More general Heisenberg groups formula_31 may be defined for higher dimensions in Euclidean space, and more generally on symplectic vector spaces. The simplest general case is the real Heisenberg group of dimension formula_32, for any integer formula_33. As a group of matrices, formula_31 (or formula_35 to indicate this is the Heisenberg group over the field formula_36 of real numbers) is defined as the group formula_37 matrices with entries in formula_36 and having the form: where This is indeed