Aharonov-Bohm effect in quantum-to-classical correspondence of the Heisenberg principle

Journal Article · Tue Apr 01 04:00:00 EST 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.67.042109· OSTI ID:20633939

Lin, D -H; Chang, J -G; Hwang, C -C ^[1]

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1. National Center for High-Performance Computing, No. 21, Nan-ke 3rd Road, Hsin-Shi, Tainan County 744, Taiwan (China)

The exact energy spectrum and wave function of a charged particle moving in the Coulomb field and Aharonov-Bohm's magnetic flux are solved by the nonintegrable phase factor. The universal formula for the matrix elements of the radial operator r{sup {alpha}} of arbitrary power {alpha} is given by an analytical solution. The difference between the classical limit of matrix elements of inverse radius in quantum mechanics and the Fourier components of the corresponding quantity for the pure Coulomb system in classical mechanics is examined in reference to the correspondence principle of Heisenberg. Explicit calculation shows that the influence of nonlocal Aharonov-Bohm effect exists even in the classical limit. The semiclassical quantization rule for systems containing the topological effect is presented in the light of Heisenberg's corresponding principle.

• OSTI ID: 20633939
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 67; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
AHARONOV-BOHM EFFECT
ANALYTICAL SOLUTION
CHARGED PARTICLES
CLASSICAL MECHANICS
COULOMB FIELD
ENERGY SPECTRA
HEISENBERG MODEL
MAGNETIC FLUX
MATRIX ELEMENTS
QUANTIZATION
QUANTUM MECHANICS
SEMICLASSICAL APPROXIMATION
TOPOLOGY
UNCERTAINTY PRINCIPLE
VISIBLE RADIATION
WAVE FUNCTIONS