The Aharonov–Bohm effect in scattering theory

Journal Article · Sun Dec 15 04:00:00 EST 2013 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2013.09.018· OSTI ID:22224271

Vlasii, N. D. ^[1]

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1. Physics Department, Taras Shevchenko National University of Kyiv, 64 Volodymyrska str., Kyiv, 01601 (Ukraine)

The Aharonov–Bohm effect is considered as a scattering event with nonrelativistic charged particles of the wavelength which is less than the transverse size of an impenetrable magnetic vortex. The quasiclassical WKB method is shown to be efficient in solving this scattering problem. We find that the scattering cross section consists of two terms, one describing the classical phenomenon of elastic reflection and another one describing the quantum phenomenon of diffraction; the Aharonov–Bohm effect is manifested as a fringe shift in the diffraction pattern. Both the classical and the quantum phenomena are independent of the choice of a boundary condition at the vortex edge, providing that probability is conserved. We show that a propagation of charged particles can be controlled by altering the flux of a magnetic vortex placed on their way. -- Highlights: •Aharonov–Bohm effect as a scattering event. •Impenetrable magnetic vortex of nonzero transverse size. •Scattering cross section is independent of a self-adjoint extension employed. •Classical phenomenon of elastic reflection and quantum phenomenon of diffraction. •Aharonov–Bohm effect as a fringe shift in the diffraction pattern.

• OSTI ID: 22224271
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Vol. 339; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
CHARGED PARTICLES
CROSS SECTIONS
DIFFRACTION
PROBABILITY
REFLECTION
VORTICES
WAVELENGTHS