dorsal/arxiv
View SchemaInverting Time-Dependent Harmonic Oscillator Potential by a Unitary Transformation and a New Class of Exactly Solvable Oscillators
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9611053 |
| URL | https://arxiv.org/abs/quant-ph/9611053 |
| DOI | 10.1103/PhysRevA.55.4084 |
| Journal | Phys.Rev. A55 (1997) 4084-4088 |
Abstract
A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass and imaginary frequency. The latter may be reduced to an ordinary harmonic oscillator by means of another unitary (canonical) transformation. A simple analysis of the resulting system leads to the identification of a previously unknown class of exactly solvable time-dependent oscillators. Furthermore, it is shown how one can apply these results to establish a canonical equivalence between some real and imaginary frequency oscillators. In particular it is shown that a harmonic oscillator whose frequency is constant and whose mass grows linearly in time is canonically equivalent with an oscillator whose frequency changes from being real to imaginary and vice versa repeatedly.
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"abstract": "A time-dependent unitary (canonical) transformation is found which maps the\nHamiltonian for a harmonic oscillator with time-dependent real mass and real\nfrequency to that of a generalized harmonic oscillator with time-dependent real\nmass and imaginary frequency. The latter may be reduced to an ordinary harmonic\noscillator by means of another unitary (canonical) transformation. A simple\nanalysis of the resulting system leads to the identification of a previously\nunknown class of exactly solvable time-dependent oscillators. Furthermore, it\nis shown how one can apply these results to establish a canonical equivalence\nbetween some real and imaginary frequency oscillators. In particular it is\nshown that a harmonic oscillator whose frequency is constant and whose mass\ngrows linearly in time is canonically equivalent with an oscillator whose\nfrequency changes from being real to imaginary and vice versa repeatedly.",
"arxiv_id": "quant-ph/9611053",
"authors": [
"Ali Mostafazadeh"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1103/PhysRevA.55.4084",
"journal_ref": "Phys.Rev. A55 (1997) 4084-4088",
"title": "Inverting Time-Dependent Harmonic Oscillator Potential by a Unitary Transformation and a New Class of Exactly Solvable Oscillators",
"url": "https://arxiv.org/abs/quant-ph/9611053"
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