Time-Dependent Diffeomorphisms as Quantum Canonical Transformations and the Time-Dependent Harmonic Oscillator

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dc.creatorMostafazadeh, Ali
dc.date1998-07-01
dc.date.accessioned2026-07-07T10:55:06Z
dc.date.available2026-07-07T10:55:06Z
dc.descriptionQuantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a previously unknown class of exactly solvable time-dependent harmonic oscillators. The Caldirola-Kanai oscillator belongs to this class. For a general time-dependent harmonic oscillator, it is shown that choosing the dilatation parameter to satisfy the classical equation of motion, one obtains the solution of the Schrödinger equation. A simple generalization of this result leads to the reduction of the Schrödinger equation to a second order ordinary differential equation whose special case is the auxiliary equation of the Lewis-Riesenfeld invariant theory. Time-evolution operator is expressed in terms of a positive real solution of this equation in a closed form, and the time-dependent position and momentum operators are calculated.
dc.descriptionPlain Latex, J. Phys. A: Math. Gen., to appear
dc.identifierhttps://arxiv.org/abs/quant-ph/9807002
dc.identifierhttp://arxiv.org/abs/quant-ph/9807002
dc.identifierJ.Phys.A31:6495-6503,1998
dc.identifierdoi:10.1088/0305-4470/31/30/014
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/186011
dc.subjectQuantum Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.titleTime-Dependent Diffeomorphisms as Quantum Canonical Transformations and the Time-Dependent Harmonic Oscillator
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