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

arXiv:hep-th/9707026

The incident wave in Aharonov-Bohm scattering wavefunction

Sahng-Kyoon Yoo, D.K. Park

Published Jul 2, 1997• 0 citations
arXivHTMLPDF

Abstract

It is shown that only the infinite angular momentum quantum states contribute to the incident wave in Aharonov-Bohm (AB) scattering. This result is clearly shown by recalculating the AB calculation with arbitrary decomposition of summation over the angular momentum quantum numbers in wave function. It is motivated from the fact that the pole contribution in the integral representation used by Jackiw is given by only the infinite angular momentum states, in which the closed contour integration involving this pole gives just the incident wave.

DOI
10.48550/arxiv.hep-th/9707026

Related papers

Some aspects of the Aharonov-Bohm effect

Walter C. Henneberger

It is shown that the Aharonov-Bohm scattering cross section diverges. This presents a problem since the range of the scattering force (Lorentz force) is finite. The cross section found by Aharonov and Bohm (AB) results whether one takes an incident wave function corresponding to particles moving in the incident direction, as was done by AB, or just takes the incident state to be a plane wave. The mechanism by which a localized force results in an infinite cross section is not clear. This is an apparent contradiction to recent proofs that electrodynamics is a local theory.

Physical Review A•Oct 1, 1980•38 citations

Aharonov–Bohm scattering: The role of the incident wave

Seiji Sakoda, Minoru Omote

The scattering problem under the influence of the Aharonov–Bohm (AB) potential is reconsidered. By solving the Lippmann–Schwinger (LS) equation we obtain the wave function of the scattering state in this system. In spite of working with a plane wave as an incident wave we obtain the same wave function as was given by Aharonov and Bohm. Another method to solve the scattering problem is given by making use of a modified version of Gordon’s idea, which was invented to consider the scattering by the Coulomb potential. These two methods give the same result, which guarantees the validity of taking an incident plane wave as usual to make an analysis of this scattering problem. The scattering problem by a solenoid of finite radius is also discussed, and we find that the vector potential of the solenoid affects the charged particles, even when the magnitude of the flux is an odd integer as well as a noninteger. It is shown that the unitarity of the S matrix holds provided that a plane wave is taken to be an incident one.

arXiv:hep-th/9603185•Journal of Mathematical Physics•Feb 1, 1997•17 citations

Partial wave analysis of the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential

M. S. Shikakhwa, Namik Kemal Pak

A partial wave analysis using the basis of the total angular momentum operator ${J}_{3}$ is carried out for the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential. It is demonstrated that the s partial wave contributes to the scattering amplitude in contrast with the case with scalar nonrelativistic particles. We suggest that this explains the fact that the first order Born amplitude of a Dirac particle coincides with the exact amplitude expanded to the same order, where it does not for a scalar particle. An interesting algebra involving the Dirac velocity operator and the angular observables is discovered and its consequences are exploited.

arXiv:hep-th/0302169•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•May 23, 2003•3 citations

Aharonov-Bohm and Coulomb Scattering Near the Forward Direction

Charles M. Sommerfield, Hisakazu Minakata

The exact wave functions that describe scattering of a charged particle by a confined magnetic field (Aharonov-Bohm effect) and by a Coulomb field are analyzed. It is well known that the usual procedure of finding asymptotic forms of these functions which admit a separation into a superposition of an incident plane wave and a circular or spherical scattered wave is problematic near the forward direction. It thus appears to be impossible to express the conservation of probability by means of an optical theorem of the usual kind. Both the total cross section and the forward scattering amplitude appear to be infinite. To address these difficulties we find a new representation for the asymptotic form of the Aharonov-Bohm wave function that is valid for all angles. Rather than try to define a cross section at forward angles, however, we work instead with the probability current and find that it is quite well behaved. The same is true for Coulomb scattering. We trace the usual difficulties to a nonuniformity of limits.

arXiv:hep-th/0006092•Jun 13, 2000•1 citation

Asymptotics of the many-whirls representation for Aharonov–Bohm scattering

Michael Berry

The previously derived decomposition of the Aharonov–Bohm (AB) wavefunction, into ‘whirling waves’ that wind different numbers of times round the flux line, is studied in detail. Asymptotic approximations are derived, describing many windings, far from the flux, and near the forward direction where the incident and scattered waves cannot be separated. The many-whirls representation gives insight into elementary explanations of the AB in terms of interference between waves passing on either side of the flux; three whirling waves suffice to give a very accurate description of the AB wave.

Journal of Physics A Mathematical and Theoretical•Aug 12, 2010•11 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
It is shown that only the infinite angular momentum quantum states contribute to the incident wave in Aharonov-Bohm (AB) scattering. This result is clearly shown by recalculating the AB calculation with arbitrary decomposition of summation over the angular momentum quantum numbers in wave function. It is motivated from the fact that the pole contribution in the integral representation used by Jackiw is given by only the infinite angular momentum states, in which the closed contour integration involving this pole gives just the incident wave.
It is shown that the Aharonov-Bohm scattering cross section diverges. This presents a problem since the range of the scattering force (Lorentz force) is finite. The cross section found by Aharonov and Bohm (AB) results whether one takes an incident wave function corresponding to particles moving in the incident direction, as was done by AB, or just takes the incident state to be a plane wave. The mechanism by which a localized force results in an infinite cross section is not clear. This is an apparent contradiction to recent proofs that electrodynamics is a local theory.
The scattering problem under the influence of the Aharonov–Bohm (AB) potential is reconsidered. By solving the Lippmann–Schwinger (LS) equation we obtain the wave function of the scattering state in this system. In spite of working with a plane wave as an incident wave we obtain the same wave function as was given by Aharonov and Bohm. Another method to solve the scattering problem is given by making use of a modified version of Gordon’s idea, which was invented to consider the scattering by the Coulomb potential. These two methods give the same result, which guarantees the validity of taking an incident plane wave as usual to make an analysis of this scattering problem. The scattering problem by a solenoid of finite radius is also discussed, and we find that the vector potential of the solenoid affects the charged particles, even when the magnitude of the flux is an odd integer as well as a noninteger. It is shown that the unitarity of the S matrix holds provided that a plane wave is taken to be an incident one.
A partial wave analysis using the basis of the total angular momentum operator J3{J}_{3}J3​ is carried out for the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential. It is demonstrated that the s partial wave contributes to the scattering amplitude in contrast with the case with scalar nonrelativistic particles. We suggest that this explains the fact that the first order Born amplitude of a Dirac particle coincides with the exact amplitude expanded to the same order, where it does not for a scalar particle. An interesting algebra involving the Dirac velocity operator and the angular observables is discovered and its consequences are exploited.
The exact wave functions that describe scattering of a charged particle by a confined magnetic field (Aharonov-Bohm effect) and by a Coulomb field are analyzed. It is well known that the usual procedure of finding asymptotic forms of these functions which admit a separation into a superposition of an incident plane wave and a circular or spherical scattered wave is problematic near the forward direction. It thus appears to be impossible to express the conservation of probability by means of an optical theorem of the usual kind. Both the total cross section and the forward scattering amplitude appear to be infinite. To address these difficulties we find a new representation for the asymptotic form of the Aharonov-Bohm wave function that is valid for all angles. Rather than try to define a cross section at forward angles, however, we work instead with the probability current and find that it is quite well behaved. The same is true for Coulomb scattering. We trace the usual difficulties to a nonuniformity of limits.
The previously derived decomposition of the Aharonov–Bohm (AB) wavefunction, into ‘whirling waves’ that wind different numbers of times round the flux line, is studied in detail. Asymptotic approximations are derived, describing many windings, far from the flux, and near the forward direction where the incident and scattered waves cannot be separated. The many-whirls representation gives insight into elementary explanations of the AB in terms of interference between waves passing on either side of the flux; three whirling waves suffice to give a very accurate description of the AB wave.
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.