Canonical Transformations in Quantum Mechanics

Details Canonical Transformations in Quantum Mechanics Canonical Transformations in Quantum Mechanics

1992-05-22

arxiv.org/abs/hep-th/9205080v2

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, McGill 92-29 (revised version--several typos fixed in examples)

Scientific paper

Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in principle, be realized quantum mechanically as a product of these transformations. It is found that the intertwining of two super-Hamiltonians is equivalent to there being a canonical transformation between them. A consequence is that the procedure for solving a differential equation can be viewed as a sequence of elementary canonical transformations trivializing the super-Hamiltonian associated to the equation. It is proposed that the quantum integrability of a system is equivalent to the existence of such a sequence.

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