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

American Journal of Physics

Spin-flips in Dirac scattering by a one-dimensional barrier

Solomon J. Glass, H. Mendlowitz

Published May 1, 1989• 2 citations
Publisher

Abstract

A Dirac particle scattered by a potential barrier varying in one dimension is treated. The incident momentum is three-dimensional. It is shown that the scattered amplitudes have contributions due to spin-flip.
DOI
10.1119/1.16004

Related papers

Low momentum scattering in the Dirac equation

Piers Kennedy, Norman Dombey

It is shown that the amplitude for reflection of a Dirac particle with arbitrarily low momentum incident on a potential of finite range is −1 and hence the transmission coefficient T = 0 in general. If, however, the potential supports a half-bound state at momentum k = 0 this result does not hold. In the case of an asymmetric potential the transmission coefficient T will be nonzero whilst for a symmetric potential T = 1. Therefore in some circumstances a Dirac particle of arbitrarily small momentum can tunnel without reflection through a potential barrier.

arXiv:hep-th/0112156•Journal of Physics A Mathematical and General•Jul 25, 2002•35 citations

Multiple Reflection in Potential-Barrier Scattering

John E. Beam

The standard quantum mechanical problem of scattering of an incident plane wave by a rectangular potential barrier in one dimension is examined from a point of view which emphasizes the multiple-scattering contributions to the reflected and transmitted, waves. This approach is used to gain insight into the phenomenon of resonant scattering of a wave packet by a potential barrier.

American Journal of Physics•Dec 1, 1970•12 citations

Scattering of identical particles by a one-dimensional Dirac delta function barrier potential: The role of statistics

P. R. Berman, Alberto G. Rojo

Scattering of non-interacting, identical bosons or fermions by a one-dimensional Dirac delta function barrier potential underlines the importance of the role of statistics (that is, whether the particles obey Fermi–Dirac or Bose–Einstein statistics) in the scattering. We consider an initial wave function for the system that corresponds to one particle incident from the left and one from the right of the potential barrier. For bosons, both particles are scattered either to the left or to the right if the intensity reflection coefficient is 1/2, provided the left and right propagating wave packets fully overlap in the scattering region. For fermions, the particles “pass through” one another, provided the left and right propagating wave packets fully overlap in the scattering region, with zero probability that both particles are scattered to the left or right, consistent with the Pauli exclusion principle.

American Journal of Physics•Sep 21, 2023•1 citation

Anomalous relativistic tunneling and exotic point interactions

P. Hejčík, T. Cheon

We examine the one-dimensional quantum scattering of a Dirac particle off relativistic potential barriers. With proper considerations of the Dirac sea, the existence of anomalous tunneling at zero incident energy is revealed for a particular type of relativistic potential having the same magnitudes and opposite signs for scalar and vector components. It is also shown that this leads to an exotic short-range limit of the potentials.

arXiv:0709.3495•Europhysics Letters (EPL)•Feb 4, 2008•8 citations

Entanglement mechanisms in one-dimensional potential scattering

Nathan L. Harshman, P Singh

When two non-relativistic particles scatter in one dimension, they can become entangled. This entanglement process is constrained by the symmetries of the scattering system and the boundary conditions on the incoming state. Applying these constraints, three different mechanisms of entanglement can be identified: the superposition of reflected and transmitted modes, momentum correlations of the reflected mode due to inversion of the relative momentum, and momentum correlations in the transmitted and reflected modes due to dependence of the scattering amplitude on the relative momentum. We consider three standard potentials, the hard core, Dirac delta, and double Dirac delta, and show that the relative importance of these mechanisms depends on the interaction and on the properties of the incoming wavefunction. We find that even when the momenta distributions of the incoming articles are sharply peaked, entanglement due to the momentum correlations generated by reflection can be quite large for particles with unequal mass.

arXiv:0712.0014•Journal of Physics A Mathematical and Theoretical•Apr 2, 2008•26 citations

Spin-dependent confinement limit of Dirac particles in three dimensions

Jian-Yuan Cheng

Unanyan, Otterbach, and Fleischhauer [Phys. Rev. A 79, 044101 (2009)] found that the confinement limit of a one-dimensional Dirac particle can be derived from the Dirac equation. The generalization of this problem to three dimensions is discussed in this paper. It shows that the three-dimensional Dirac particle in vector and scalar potentials has a confinement limit proportional to the modulus of expectation value of spin. This result obtained in Dirac equation is applicable for any Dirac particle confined in a finite region of space, even when vector and scalar potentials of quite general character are present. In addition, a Dirac particle confined in Lorentz scalar potential is discussed.

Physical Review A•Sep 18, 2015•0 citations
It is shown that the amplitude for reflection of a Dirac particle with arbitrarily low momentum incident on a potential of finite range is −1 and hence the transmission coefficient T = 0 in general. If, however, the potential supports a half-bound state at momentum k = 0 this result does not hold. In the case of an asymmetric potential the transmission coefficient T will be nonzero whilst for a symmetric potential T = 1. Therefore in some circumstances a Dirac particle of arbitrarily small momentum can tunnel without reflection through a potential barrier.
Scattering of non-interacting, identical bosons or fermions by a one-dimensional Dirac delta function barrier potential underlines the importance of the role of statistics (that is, whether the particles obey Fermi–Dirac or Bose–Einstein statistics) in the scattering. We consider an initial wave function for the system that corresponds to one particle incident from the left and one from the right of the potential barrier. For bosons, both particles are scattered either to the left or to the right if the intensity reflection coefficient is 1/2, provided the left and right propagating wave packets fully overlap in the scattering region. For fermions, the particles “pass through” one another, provided the left and right propagating wave packets fully overlap in the scattering region, with zero probability that both particles are scattered to the left or right, consistent with the Pauli exclusion principle.
When two non-relativistic particles scatter in one dimension, they can become entangled. This entanglement process is constrained by the symmetries of the scattering system and the boundary conditions on the incoming state. Applying these constraints, three different mechanisms of entanglement can be identified: the superposition of reflected and transmitted modes, momentum correlations of the reflected mode due to inversion of the relative momentum, and momentum correlations in the transmitted and reflected modes due to dependence of the scattering amplitude on the relative momentum. We consider three standard potentials, the hard core, Dirac delta, and double Dirac delta, and show that the relative importance of these mechanisms depends on the interaction and on the properties of the incoming wavefunction. We find that even when the momenta distributions of the incoming articles are sharply peaked, entanglement due to the momentum correlations generated by reflection can be quite large for particles with unequal mass.
Unanyan, Otterbach, and Fleischhauer [Phys. Rev. A 79, 044101 (2009)] found that the confinement limit of a one-dimensional Dirac particle can be derived from the Dirac equation. The generalization of this problem to three dimensions is discussed in this paper. It shows that the three-dimensional Dirac particle in vector and scalar potentials has a confinement limit proportional to the modulus of expectation value of spin. This result obtained in Dirac equation is applicable for any Dirac particle confined in a finite region of space, even when vector and scalar potentials of quite general character are present. In addition, a Dirac particle confined in Lorentz scalar potential is discussed.