dorsal/arxiv
View SchemaExact quantization of nonsolvable potentials: the role of the quantum phase beyond the semiclassical approximation
| Authors | A. Matzkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411084 |
| URL | https://arxiv.org/abs/quant-ph/0411084 |
Abstract
Semiclassical quantization is exact only for the so called \emph{solvable} potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the semiclassical phase, given by a series in $\hbar$, yields more or less approximate results and eventually diverges due to the asymptotic nature of the expansion. A quantum phase is derived to bypass these shortcomings. It achieves exact quantization of nonsolvable potentials and allows to obtain the quantum wavefunction while locally approaching the best pre-divergent semiclassical expansion. An iterative procedure allowing to implement practical calculations with a modest computational cost is also given. The theory is illustrated on two examples for which the limitations of the semiclassical approach were recently highlighted: cold atomic collisions and anharmonic oscillators in the nonperturbative regime.
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"abstract": "Semiclassical quantization is exact only for the so called \\emph{solvable}\npotentials, such as the harmonic oscillator. In the \\emph{nonsolvable} case the\nsemiclassical phase, given by a series in $\\hbar$, yields more or less\napproximate results and eventually diverges due to the asymptotic nature of the\nexpansion. A quantum phase is derived to bypass these shortcomings. It achieves\nexact quantization of nonsolvable potentials and allows to obtain the quantum\nwavefunction while locally approaching the best pre-divergent semiclassical\nexpansion. An iterative procedure allowing to implement practical calculations\nwith a modest computational cost is also given. The theory is illustrated on\ntwo examples for which the limitations of the semiclassical approach were\nrecently highlighted: cold atomic collisions and anharmonic oscillators in the\nnonperturbative regime.",
"arxiv_id": "quant-ph/0411084",
"authors": [
"A. Matzkin"
],
"categories": [
"quant-ph"
],
"title": "Exact quantization of nonsolvable potentials: the role of the quantum phase beyond the semiclassical approximation",
"url": "https://arxiv.org/abs/quant-ph/0411084"
},
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