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In physics, the Schrödinger picture or Schrödinger representation is a formulation of quantum mechanics in which the state vectors evolve in time, but the operators (observables and others) are mostly constant with respect to time (an exception is the Hamiltonian which may change if the potential changes).
All three of these choices are valid; the first gives the Schrödinger picture, the second the Heisenberg picture, and the third the interaction picture. The Schrödinger picture is useful when dealing with a time-independent Hamiltonian H , that is, ∂ t H = 0 {\displaystyle \partial _{t}H=0} .
In the Schrödinger picture, the wave function or field is the solution to the Schrödinger equation; = ^ one of the postulates of quantum mechanics. All relativistic wave equations can be constructed by specifying various forms of the Hamiltonian operator Ĥ describing the quantum system .
Any possible choice of parts will yield a valid interaction picture; but in order for the interaction picture to be useful in simplifying the analysis of a problem, the parts will typically be chosen so that H 0,S is well understood and exactly solvable, while H 1,S contains some harder-to-analyze perturbation to this system.
In physics, the Heisenberg picture or Heisenberg representation [1] is a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which observables incorporate a dependency on time, but the states are time-independent. It stands in contrast to the Schrödinger picture in which observables are constant and the states evolve ...
In fact, for very positive times t the factor in a Schrödinger picture state forces one to close the contour on the lower half-plane. The pole in the ( ϕ , V ψ ± ) {\displaystyle (\phi ,V\psi ^{\pm })} from the Lippmann–Schwinger equation reflects the time-uncertainty of the interaction, while that in the wavepackets weight function ...
The Schrödinger functional is, in its most basic form, the time translation generator of state wavefunctionals. In layman's terms, it defines how a system of quantum particles evolves through time and what the subsequent systems look like.
In the Schrödinger picture, the unitary operators are taken to act upon the system's quantum state, whereas in the Heisenberg picture, the time dependence is incorporated into the observables instead.