Comparing classical and quantum probability distributions for an asymmetric infinite well

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dc.creatorDoncheski, M. A.
dc.creatorRobinett, R. W.
dc.date2003-07-02
dc.date.accessioned2026-07-07T06:07:14Z
dc.date.available2026-07-07T06:07:14Z
dc.descriptionWe compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum probability distributions agree fairly well, even for relatively small quantum numbers, except for anomalous cases which are due to the unphysical nature of the potential. We are able to derive upper and lower bounds on the differences between the quantum and classical results. We also qualitatively discuss the momentum-space probability densities for this system using intuitive ideas about how much time a classical particle spends in various parts of the well. This system provides an excellent example of a non-trivial, but tractable, quantum mechanical bound state problem where the correlations between the amplitude and curvature of quantum mechanical wavefunctions can be easily compared to classical intuition about particle motion, with quantitative success, but also warning of possible surprises in non-physical limiting cases.
dc.description17 pages, 6 separate .ps figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0307014
dc.identifierhttp://arxiv.org/abs/quant-ph/0307014
dc.identifierEur. J. Phys. 21, 217 (2000)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/91219
dc.subjectQuantum Physics
dc.titleComparing classical and quantum probability distributions for an asymmetric infinite well
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