Exact quantization of nonsolvable potentials: the role of the quantum phase beyond the semiclassical approximation

Simple item page
dc.creatorMatzkin, A.
dc.date2004-11-11
dc.date.accessioned2026-07-07T06:11:29Z
dc.date.available2026-07-07T06:11:29Z
dc.descriptionSemiclassical 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.
dc.identifierhttps://arxiv.org/abs/quant-ph/0411084
dc.identifierhttp://arxiv.org/abs/quant-ph/0411084
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/92502
dc.subjectQuantum Physics
dc.titleExact quantization of nonsolvable potentials: the role of the quantum phase beyond the semiclassical approximation
dc.typetext

Files

Collections

arXiv