TY - JOUR

T1 - Comparing classical and quantum probability distributions for an asymmetric infinite well

AU - Doncheski, M. A.

AU - Robinett, R. W.

PY - 2000/5/1

Y1 - 2000/5/1

N2 - We 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 arise due to the unphysical nature of the potential. We are able to derive upper and lower hounds 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 the amount of 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.

AB - We 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 arise due to the unphysical nature of the potential. We are able to derive upper and lower hounds 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 the amount of 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.

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U2 - 10.1088/0143-0807/21/3/303

DO - 10.1088/0143-0807/21/3/303

M3 - Article

AN - SCOPUS:0347107298

VL - 21

SP - 217

EP - 228

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 3

ER -