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:physics/0202020

Quantum effects in the scattering by the magnetic field of a solenoid

Gabriela Murguía, Moreno, Matias

Published Feb 7, 2002• 0 citations
arXivHTMLPDF

Abstract

We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by the magnetic field of a solenoid. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non relativistic case. We show that taking pr_0 sin(theta/2) << 1 in our expression of the differential cross section it reduces to that one reported by AB, and if additionally we assume theta << 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in hbar as opposed to our initial result. We analyse the singular behavior in hbar and show that the perturbative Planck limit (hbar -> 0) is consistent, contrarily to those of the AB and LL expressions.

DOI
10.48550/arxiv.physics/0202020

Related papers

Classical limit for the scattering of Dirac particles in a magnetic field

G Murgu a, M Moreno

We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by a solenoidal magnetic field. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non-relativistic case. We show that taking pr 0 |sin (θ/2)|/ ≪ 1 in our expression of the differential cross section it reduces to the one reported by AB, and if additionally we assume θ ≪ 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in as opposed to our initial result. We analyse the singular behaviour in and show that the perturbative Planck limit ( → 0) is consistent, in contrast to those of the AB and LL expressions. We also discuss the scattering in a uniform and constant magnetic field, which resembles some features of QCD.

arXiv:quant-ph/0211195•Journal of Physics A Mathematical and General•Feb 26, 2003•1 citation

Quantum versus classical scattering of Dirac particles by a solenoidal magnetic field and the correspondence principle

Gabriela Murguía, Moreno, Matias, Manuel Torres

We present a detailed analysis of the scattering of charged particles by the magnetic field of a long solenoid of constant magnetic flux and finite radius. We study the relativistic and non-relativistic quantum and classical scenarios. The classical limit of the perturbative quantum expressions, understood as the Planck's limit (making $\hbar$ going to zero) is analyzed and compared with the classical result. The classical cross section shows a general non-symmetric behavior with respect to the scattering angle in contradistinction to the quantum calculations performed so far. The various regimes analyzed show that the quantum cross sections do not satisfy the correspondence principle: they do not reduce to the classical result in any considered limit, an argument in favor of the interpretation of the process as a purely quantum phenomenon. We conclude that in order to restore the classical correspondence of the phenomenon, a complete non-perturbative quantum calculation for a finite solenoid radius is required.

arXiv:quant-ph/0407123•Jul 15, 2004•0 citations

Perturbative Quantum Analysis and Classical Limit of the Electron Scattering by a Solenoidal Magnetic Field

Gabriela Murguía, Matías Moreno, Manuel Torres

A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non‐relativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable non‐perturbative methodology should be applied.

arXiv:0903.0427•Mexican School of Particles and Fields•Jan 1, 2009•0 citations

Scattering of scalar and Dirac particles by a magnetic tube of finite radius

Vladimir D. Skarzhinsky, Jürgen Audretsch

We consider the Dirac equation in cylindrically symmetric magnetic fields and find its normal modes as eigenfunctions of a complete set of commuting operators. This set consists of the Dirac operator itself, the $z$-components of the linear and the total angular momenta, and of one of the possible spin polarization operators. The spin structure of the solution is completely fixed independently of the radial distribution of the magnetic field which influences only the radial modes. We solve explicitly the radial equations for the uniform magnetic field inside a solenoid of a finite radius and consider in detail the scattering of scalar and Dirac particles in this field. For particles with low energy the scattering cross section coincides with the Aharonov-Bohm scattering cross section. We work out the first order corrections to this result caused by the fact that the solenoid radius is finite. At high energies we obtain the classical result for the scattering cross section.

•Jan 1, 1997•6 citations

Scattering of scalar and Dirac particles by a magnetic tube of finite radius

Vladimir D Skarzhinsky, Jürgen Audretsch

We consider the Dirac equation in cylindrically symmetric magnetic fields and find its normal modes as eigenfunctions of a complete set of commuting operators. This set consists of the Dirac operator itself, the z-components of the linear and the total angular momenta, and of one of the possible spin polarization operators. The spin structure of the solution is completely fixed independently of the radial distribution of the magnetic field which influences only the radial modes. We solve explicitly the radial equations for the uniform magnetic field inside a solenoid of finite radius and consider in detail the scattering of scalar and Dirac particles in this field. For particles with low energy the scattering cross section coincides with the Aharonov - Bohm scattering cross section. We work out the first-order corrections to this result caused by the fact that the solenoid radius is finite. At high energies we obtain the classical result for the scattering cross section.

arXiv:hep-th/9709086•Journal of Physics A Mathematical and General•Nov 7, 1997•6 citations

Momentum-transfer scattering cross section and the Aharonov-Bohm effect on a toroidal solenoid

Vladimir Lvovich Lyuboshitz, Vladimir Lvovich Lyuboshitz

The quantum-mechanical Aharonov-Bohm effect in the diffraction of charged particles by a toroidal solenoid containing a magnetic field is investigated. The total and differential elastic scattering cross sections depend on the magnetic flux inside the solenoid, even in the presence of a “black” ring-shaped screen which prevents charged particles from entering the region where the magnetic field is localized. Relations describing the momentum-transfer cross section for the elastic scattering of charged particles by a toroidal solenoid are obtained in the eikonal approximation and in a unitary model of scattering with a sharp jump in the partial amplitudes. The momentum-transfer scattering cross section is proportional to the average transfer of the longitudinal momentum of the scattered particle and can be expressed in terms of a force operator. It is shown that in the absence of a screen the momentum-transfer scattering cross section of toroidal solenoid is indeed determined only by the part of the incident beam that intersects the inner region of the toroidal solenoid, where the magnetic field intensity and, therefore, the Lorentz force are nonzero. At the same time, the momentum-transfer cross section for the scattering of charged particles by a toroidal solenoid covered by a “black” ring-shaped screen does not depend on the magnetic flux inside the solenoid and is identical to the momentum-transfer cross section for diffraction by the same screen. The contribution from scattering by an opening in the screen, which depends on the magnetic flux, is completely compensated by the contribution of the interference of the scattering amplitudes of the opening and the “black” screen.

Journal of Experimental and Theoretical Physics•Oct 1, 2000•2 citations
We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by the magnetic field of a solenoid. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non relativistic case. We show that taking pr_0 sin(theta/2) << 1 in our expression of the differential cross section it reduces to that one reported by AB, and if additionally we assume theta << 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in hbar as opposed to our initial result. We analyse the singular behavior in hbar and show that the perturbative Planck limit (hbar -> 0) is consistent, contrarily to those of the AB and LL expressions.
We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by a solenoidal magnetic field. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non-relativistic case. We show that taking pr 0 |sin (θ/2)|/ ≪ 1 in our expression of the differential cross section it reduces to the one reported by AB, and if additionally we assume θ ≪ 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in as opposed to our initial result. We analyse the singular behaviour in and show that the perturbative Planck limit ( → 0) is consistent, in contrast to those of the AB and LL expressions. We also discuss the scattering in a uniform and constant magnetic field, which resembles some features of QCD.
We present a detailed analysis of the scattering of charged particles by the magnetic field of a long solenoid of constant magnetic flux and finite radius. We study the relativistic and non-relativistic quantum and classical scenarios. The classical limit of the perturbative quantum expressions, understood as the Planck's limit (making ℏ\hbarℏ going to zero) is analyzed and compared with the classical result. The classical cross section shows a general non-symmetric behavior with respect to the scattering angle in contradistinction to the quantum calculations performed so far. The various regimes analyzed show that the quantum cross sections do not satisfy the correspondence principle: they do not reduce to the classical result in any considered limit, an argument in favor of the interpretation of the process as a purely quantum phenomenon. We conclude that in order to restore the classical correspondence of the phenomenon, a complete non-perturbative quantum calculation for a finite solenoid radius is required.
A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non‐relativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable non‐perturbative methodology should be applied.
We consider the Dirac equation in cylindrically symmetric magnetic fields and find its normal modes as eigenfunctions of a complete set of commuting operators. This set consists of the Dirac operator itself, the zzz-components of the linear and the total angular momenta, and of one of the possible spin polarization operators. The spin structure of the solution is completely fixed independently of the radial distribution of the magnetic field which influences only the radial modes. We solve explicitly the radial equations for the uniform magnetic field inside a solenoid of a finite radius and consider in detail the scattering of scalar and Dirac particles in this field. For particles with low energy the scattering cross section coincides with the Aharonov-Bohm scattering cross section. We work out the first order corrections to this result caused by the fact that the solenoid radius is finite. At high energies we obtain the classical result for the scattering cross section.
We consider the Dirac equation in cylindrically symmetric magnetic fields and find its normal modes as eigenfunctions of a complete set of commuting operators. This set consists of the Dirac operator itself, the z-components of the linear and the total angular momenta, and of one of the possible spin polarization operators. The spin structure of the solution is completely fixed independently of the radial distribution of the magnetic field which influences only the radial modes. We solve explicitly the radial equations for the uniform magnetic field inside a solenoid of finite radius and consider in detail the scattering of scalar and Dirac particles in this field. For particles with low energy the scattering cross section coincides with the Aharonov - Bohm scattering cross section. We work out the first-order corrections to this result caused by the fact that the solenoid radius is finite. At high energies we obtain the classical result for the scattering cross section.
The quantum-mechanical Aharonov-Bohm effect in the diffraction of charged particles by a toroidal solenoid containing a magnetic field is investigated. The total and differential elastic scattering cross sections depend on the magnetic flux inside the solenoid, even in the presence of a “black” ring-shaped screen which prevents charged particles from entering the region where the magnetic field is localized. Relations describing the momentum-transfer cross section for the elastic scattering of charged particles by a toroidal solenoid are obtained in the eikonal approximation and in a unitary model of scattering with a sharp jump in the partial amplitudes. The momentum-transfer scattering cross section is proportional to the average transfer of the longitudinal momentum of the scattered particle and can be expressed in terms of a force operator. It is shown that in the absence of a screen the momentum-transfer scattering cross section of toroidal solenoid is indeed determined only by the part of the incident beam that intersects the inner region of the toroidal solenoid, where the magnetic field intensity and, therefore, the Lorentz force are nonzero. At the same time, the momentum-transfer cross section for the scattering of charged particles by a toroidal solenoid covered by a “black” ring-shaped screen does not depend on the magnetic flux inside the solenoid and is identical to the momentum-transfer cross section for diffraction by the same screen. The contribution from scattering by an opening in the screen, which depends on the magnetic flux, is completely compensated by the contribution of the interference of the scattering amplitudes of the opening and the “black” screen.