Universal Formula for the Expectation Value of the Radial Operator under the Aharonov-Bohm Flux and the Coulomb Field

2002/10/14 by W. F. Kao, Yi-Chun Kao, Y. M. Kao +5
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Spectral Theory in Mathematical Physics #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0210106

11 pages

arxiv created 2002/10/14 · openalex publication_date 2002/10/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^λ> (-∞ ≤ λ≤ ∞) 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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