Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Aharonov-Bohm scattering amplitude

C. R. Hägen

Published Mar 15, 1990• 63 citations
Publisher

Abstract

The two principal approaches to the quantum-mechanical calculation of scattering by flux tubes in two spatial dimensions are reviewed and corrections made where needed. It is noted that even when appropriate care is taken the standard phase-shift method fails to agree with the (corrected) Aharonov-Bohm result. The discrepancy is resolved by noting that the former approach requires an improper interchange of a limit and a summation. That interchange is justified only when the phase shifts go to zero sufficiently rapidly as the angular momentum becomes arbitrarily large, a condition which fails to hold in this particular scattering problem.

DOI
10.1103/physrevd.41.2015

Related papers

Aharonov-Bohm scattering on two parallel flux tubes of the same magnetic flux

Zhi-Yu Cu, Qian Shang-Wu

The problem of Aharonov-Bohm scattering on two parallel flux tubes of the same magnetic flux is solved exactly and the differential cross section is calculated.

Journal of Physics A Mathematical and General•Sep 21, 1990•2 citations

Scattering amplitude in the Aharonov-Bohm gauge field

Paola Giacconi A, Fabio Maltoni B, Roberto Soldati

A general expression for the scattering amplitude of nonrelativistic spinless particles in the Aharonov-Bohm gauge potential is obtained within the time-independent formalism. The result is valid also in the forward direction as well as for any choice of the boundary conditions on the wave function at the flux tube position. \textcopyright{} 1996 The American Physical Society.

arXiv:hep-th/9509003•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jan 15, 1996•17 citations

Asymptotic behavior of scattering amplitudes in magnetic fields at large separation

Hiroshi T. ITO, Hideo Tamura

Magnetic potentials have a direct significance to the motion of particles in quantum mechanics. This is known as the Aharonov-Bohm effect. We study this quantum property in the scattering by two magnetic fields at large separation in two dimensions. We derive the asymptotic formula of scattering amplitude when the distance between the centers of two fields goes to infinity. The result depends on the fluxes of fields and on incident and final directions. We here consider only the simple case that at least one of two fluxes is zero.

Journal of the Mathematical Society of Japan•Jul 1, 2001•0 citations

Perturbation theory and the Aharonov-Bohm effect

C. R. Hägen

The perturbation theory expansion of the Aharonov-Bohm scattering amplitude has previously been studied in the context of quantum mechanics for spin-0 and spin-1/2 particles as well as in Galilean covariant field theory. This problem is reconsidered in the framework of the model in which the flux line is considered to have a finite radius which is shrunk to zero at the end of the calculation. General agreement with earlier results is obtained but with the advantage of a treatment which unifies all the various subcases.

arXiv:hep-th/9503032•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Aug 15, 1995•18 citations

Boundary conditions in the Aharonov-Bohm scattering of Dirac particles and the effect of Coulomb interaction

Francisco Antônio Bezerra Coutinho, J. Fernando Perez

We consider the question of the physically correct choice of the boundary conditions, and therefore of the dynamics, for the scattering of spin-\textonehalf{} particles by a thread of magnetic flux. It is shown that even when the problem is approached by first considering a source of finite radius $R$, the resulting dynamics is a consequence of how much penetration of the wave function inside the tube one chooses to allow. (The indeterminacy in the boundary condition occurs for one value of the total angular momentum for a given value of the flux.) If a Coulomb interaction of the particle with the sources is introduced in the problem, the above-mentioned indeterminacy is enlarged. We show that for a given value of the flux there are now at least two values of the angular momentum $n$ for which the indeterminacy occurs.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jul 15, 1993•17 citations

Aharonov-Bohm scattering of massive spin-one particles

C. R. Hägen, S. Ramaswamy

The Aharonov-Bohm scattering of massive spin-one particles is computed. Starting from the relativistic wave equation for a charged, massive spin-one particle, a reduction to two spatial dimensions is made, consistent with the standard Aharonov-Bohm (AB) geometry. It is found that the problem consists of the independent scattering of the three vector-meson spins. While the amplitude for the spin-0 mode is trivially identical to the AB amplitude, the same result is obtained for the spin-up and spin-down components, in sharp contrast to the corresponding result for the spin-1/2 AB amplitude. This can be traced to the fact that the Hamiltonian is unbounded as a consequence of the presence of a \ensuremath{\delta}-function term in the potential. In the Galilean limit it is found that the amplitude of the nonzero-spin components is identical to the spin-1/2 amplitude in that limit, in agreement with a general claim made earlier by one of the authors. The Galilean limit of the spin-one AB cross section is found to be modified and calculations for some pure-state polarizations are presented.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Nov 15, 1990•11 citations
The two principal approaches to the quantum-mechanical calculation of scattering by flux tubes in two spatial dimensions are reviewed and corrections made where needed. It is noted that even when appropriate care is taken the standard phase-shift method fails to agree with the (corrected) Aharonov-Bohm result. The discrepancy is resolved by noting that the former approach requires an improper interchange of a limit and a summation. That interchange is justified only when the phase shifts go to zero sufficiently rapidly as the angular momentum becomes arbitrarily large, a condition which fails to hold in this particular scattering problem.
Magnetic potentials have a direct significance to the motion of particles in quantum mechanics. This is known as the Aharonov-Bohm effect. We study this quantum property in the scattering by two magnetic fields at large separation in two dimensions. We derive the asymptotic formula of scattering amplitude when the distance between the centers of two fields goes to infinity. The result depends on the fluxes of fields and on incident and final directions. We here consider only the simple case that at least one of two fluxes is zero.
The perturbation theory expansion of the Aharonov-Bohm scattering amplitude has previously been studied in the context of quantum mechanics for spin-0 and spin-1/2 particles as well as in Galilean covariant field theory. This problem is reconsidered in the framework of the model in which the flux line is considered to have a finite radius which is shrunk to zero at the end of the calculation. General agreement with earlier results is obtained but with the advantage of a treatment which unifies all the various subcases.
We consider the question of the physically correct choice of the boundary conditions, and therefore of the dynamics, for the scattering of spin-\textonehalf{} particles by a thread of magnetic flux. It is shown that even when the problem is approached by first considering a source of finite radius RRR, the resulting dynamics is a consequence of how much penetration of the wave function inside the tube one chooses to allow. (The indeterminacy in the boundary condition occurs for one value of the total angular momentum for a given value of the flux.) If a Coulomb interaction of the particle with the sources is introduced in the problem, the above-mentioned indeterminacy is enlarged. We show that for a given value of the flux there are now at least two values of the angular momentum nnn for which the indeterminacy occurs.
The Aharonov-Bohm scattering of massive spin-one particles is computed. Starting from the relativistic wave equation for a charged, massive spin-one particle, a reduction to two spatial dimensions is made, consistent with the standard Aharonov-Bohm (AB) geometry. It is found that the problem consists of the independent scattering of the three vector-meson spins. While the amplitude for the spin-0 mode is trivially identical to the AB amplitude, the same result is obtained for the spin-up and spin-down components, in sharp contrast to the corresponding result for the spin-1/2 AB amplitude. This can be traced to the fact that the Hamiltonian is unbounded as a consequence of the presence of a \ensuremath{\delta}-function term in the potential. In the Galilean limit it is found that the amplitude of the nonzero-spin components is identical to the spin-1/2 amplitude in that limit, in agreement with a general claim made earlier by one of the authors. The Galilean limit of the spin-one AB cross section is found to be modified and calculations for some pure-state polarizations are presented.