On a Class of Quantum Canonical Transformations and the Time-Dependent Harmonic Oscillator

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dc.creatorMostafazadeh, Ali
dc.date1996-12-12
dc.date.accessioned2026-07-07T06:14:07Z
dc.date.available2026-07-07T06:14:07Z
dc.descriptionQuantum canonical transformations corresponding to the action of the unitary operator $e^{iε(t)\sqrt{f(x)}p\sqrt{f(x)}}$ is studied. It is shown that for $f(x)=x$, the effect of this transformation is to rescale the position and momentum operators by $e^{ε(t)}$ and $e^{-ε(t)}$, respectively. This transformation is shown to lead to the identification of a previously unknown class of exactly solvable time-dependent harmonic oscillators. It turns out that the Caldirola-Kanai oscillator whose mass is given by $m=m_0 e^{γt}$, belongs to this class. It is also shown that for arbitrary $f(x)$, this canonical transformations map the dynamics of a free particle with constant mass to that of free particle with a position-dependent mass. In other words, they lead to a change of the metric of the space.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/9612038
dc.identifierhttp://arxiv.org/abs/quant-ph/9612038
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/93341
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.titleOn a Class of Quantum Canonical Transformations and the Time-Dependent Harmonic Oscillator
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