dorsal/arxiv
View SchemaComparing classical and quantum probability distributions for an asymmetric infinite well
| Authors | M. A. Doncheski, R. W. Robinett |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307014 |
| URL | https://arxiv.org/abs/quant-ph/0307014 |
| Journal | Eur. J. Phys. 21, 217 (2000) |
Abstract
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 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.
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"abstract": "We compare the classical and quantum mechanical position-space probability\ndensities for a particle in an asymmetric infinite well. In an idealized system\nwith a discontinuous step in the middle of the well, the classical and quantum\nprobability distributions agree fairly well, even for relatively small quantum\nnumbers, except for anomalous cases which are due to the unphysical nature of\nthe potential. We are able to derive upper and lower bounds on the differences\nbetween the quantum and classical results. We also qualitatively discuss the\nmomentum-space probability densities for this system using intuitive ideas\nabout how much time a classical particle spends in various parts of the well.\nThis system provides an excellent example of a non-trivial, but tractable,\nquantum mechanical bound state problem where the correlations between the\namplitude and curvature of quantum mechanical wavefunctions can be easily\ncompared to classical intuition about particle motion, with quantitative\nsuccess, but also warning of possible surprises in non-physical limiting cases.",
"arxiv_id": "quant-ph/0307014",
"authors": [
"M. A. Doncheski",
"R. W. Robinett"
],
"categories": [
"quant-ph"
],
"journal_ref": "Eur. J. Phys. 21, 217 (2000)",
"title": "Comparing classical and quantum probability distributions for an asymmetric infinite well",
"url": "https://arxiv.org/abs/quant-ph/0307014"
},
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