dorsal/arxiv
View SchemaUniversal Formula for the Expectation Value of the Radial Operator under the Aharonov-Bohm Flux and the Coulomb Field
| Authors | W. F. Kao, Y. M. Kao, D. H. Lin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210106 |
| URL | https://arxiv.org/abs/quant-ph/0210106 |
Abstract
A useful and universal formula for the expectation value of the radial operator in the presence of the Aharonov-Bohm flux and the Coulomb Field is established. We find that the expectation value $< r^{\lambda}>$ $(-\infty \leq \lambda \leq \infty)$ is greatly affected due to the non-local effect of the magnetic flux although the Aharonov-Bohm flux does not have any dynamical significance in classical mechanics. In particular, the quantum fluctuation increases in the presence of the magnetic flux due to the Aharonov-Bohm effect. In addition, the Virial theory in quantum mechanics is also constructed for the spherically symmetric system under the Aharonov-Bohm effect.
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"date_created": "2026-03-02T18:01:55.390000Z",
"date_modified": "2026-03-02T18:01:55.390000Z",
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"abstract": "A useful and universal formula for the expectation value of the radial\noperator in the presence of the Aharonov-Bohm flux and the Coulomb Field is\nestablished. We find that the expectation value $\u003c r^{\\lambda}\u003e$ $(-\\infty \\leq\n\\lambda \\leq \\infty)$ is greatly affected due to the non-local effect of the\nmagnetic flux although the Aharonov-Bohm flux does not have any dynamical\nsignificance in classical mechanics. In particular, the quantum fluctuation\nincreases in the presence of the magnetic flux due to the Aharonov-Bohm effect.\nIn addition, the Virial theory in quantum mechanics is also constructed for the\nspherically symmetric system under the Aharonov-Bohm effect.",
"arxiv_id": "quant-ph/0210106",
"authors": [
"W. F. Kao",
"Y. M. Kao",
"D. H. Lin"
],
"categories": [
"quant-ph"
],
"title": "Universal Formula for the Expectation Value of the Radial Operator under the Aharonov-Bohm Flux and the Coulomb Field",
"url": "https://arxiv.org/abs/quant-ph/0210106"
},
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