dorsal/arxiv
View SchemaEigenvalue Problem for Schroedinger Operators and Time-Dependent Harmonic Oscillator
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9706056 |
| URL | https://arxiv.org/abs/quant-ph/9706056 |
Abstract
It is shown that the eigenvalue problem for the Hamiltonians of the standard form, $H=p^2/(2m)+V(x)$, is equivalent to the classical dynamical equation for certain harmonic oscillators with time-dependent frequency. This is another indication of the central role played by time-dependent harmonic oscillators in quantum mechanics. The utility of the known results for eigenvalue problem in the solution of the dynamical equations of a class of time-dependent harmonic oscillators is also pointed out.
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"abstract": "It is shown that the eigenvalue problem for the Hamiltonians of the standard\nform, $H=p^2/(2m)+V(x)$, is equivalent to the classical dynamical equation for\ncertain harmonic oscillators with time-dependent frequency. This is another\nindication of the central role played by time-dependent harmonic oscillators in\nquantum mechanics. The utility of the known results for eigenvalue problem in\nthe solution of the dynamical equations of a class of time-dependent harmonic\noscillators is also pointed out.",
"arxiv_id": "quant-ph/9706056",
"authors": [
"Ali Mostafazadeh"
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"title": "Eigenvalue Problem for Schroedinger Operators and Time-Dependent Harmonic Oscillator",
"url": "https://arxiv.org/abs/quant-ph/9706056"
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