dorsal/arxiv
View SchemaOn a Class of Quantum Canonical Transformations and the Time-Dependent Harmonic Oscillator
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9612038 |
| URL | https://arxiv.org/abs/quant-ph/9612038 |
Abstract
Quantum canonical transformations corresponding to the action of the unitary operator $e^{i\epsilon(t)\sqrt{f(x)}p\sqrt{f(x)}}$ is studied. It is shown that for $f(x)=x$, the effect of this transformation is to rescale the position and momentum operators by $e^{\epsilon(t)}$ and $e^{-\epsilon(t)}$, 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 $m=m_0 e^{\gamma t}$, 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.
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"abstract": "Quantum canonical transformations corresponding to the action of the unitary\noperator $e^{i\\epsilon(t)\\sqrt{f(x)}p\\sqrt{f(x)}}$ is studied. It is shown that\nfor $f(x)=x$, the effect of this transformation is to rescale the position and\nmomentum operators by $e^{\\epsilon(t)}$ and $e^{-\\epsilon(t)}$, respectively.\nThis transformation is shown to lead to the identification of a previously\nunknown class of exactly solvable time-dependent harmonic oscillators. It turns\nout that the Caldirola-Kanai oscillator whose mass is given by $m=m_0 e^{\\gamma\nt}$, belongs to this class. It is also shown that for arbitrary $f(x)$, this\ncanonical transformations map the dynamics of a free particle with constant\nmass to that of free particle with a position-dependent mass. In other words,\nthey lead to a change of the metric of the space.",
"arxiv_id": "quant-ph/9612038",
"authors": [
"Ali Mostafazadeh"
],
"categories": [
"quant-ph",
"hep-th"
],
"title": "On a Class of Quantum Canonical Transformations and the Time-Dependent Harmonic Oscillator",
"url": "https://arxiv.org/abs/quant-ph/9612038"
},
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