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Interaction picture : ウィキペディア英語版
Interaction picture

In quantum mechanics, the interaction picture (also known as the Dirac picture) is an intermediate representation between the Schrödinger picture and the Heisenberg picture. Whereas in the other two pictures either the state vector or the operators carry time dependence, in the interaction picture both carry part of the time dependence of observables.〔Albert Messiah (1966). ''Quantum Mechanics'', North Holland, John Wiley & Sons. ISBN 0486409244 ; J. J. Sakurai (1994). ''Modern Quantum Mechanics'' (Addison-Wesley) ISBN 9780201539295 .〕 The interaction picture is useful in dealing with changes to the wave functions and observable due to interactions. Most field theoretical calculations〔J. W. Negele, H. Orland (1988), Quantum Many-particle Systems, ISBN 0738200522〕 use the interaction representation because they construct the solution to the many body Schrödinger equation as the solution to the free particle problem plus some unknown interaction parts.
Equations that include operators acting at different times, which hold in the interaction picture, don't necessarily hold in the Schrödinger or the Heisenberg picture. This is because time-dependent unitary transformations relate operators in one picture to the analogous operators in the others.
==Definition==

Operators and state vectors in the interaction picture are related by a change of basis (unitary transformation) to those same operators and state vectors in the Schrödinger picture.
To switch into the interaction picture, we divide the Schrödinger picture Hamiltonian into two parts,
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.
If the Hamiltonian has ''explicit time-dependence'' (for example, if the quantum system interacts with an applied external electric field that varies in time), it will usually be advantageous to include the explicitly time-dependent terms with ''H''1,S, leaving ''H''0,S time-independent. We proceed assuming that this is the case. If there ''is'' a context in which it makes sense to have ''H''0,S be time-dependent, then one can proceed by replacing e^ by the corresponding time-evolution operator in the definitions below.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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