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

Scattering from a nonsymmetric potential in one dimension as a coupled-channel problem

Yozo Nogami, Carl K. Ross

Published Jul 1, 1996• 50 citations
Publisher

Abstract

We study the partial-wave description of scattering of a particle from a one-dimensional potential in quantum mechanics. There are two partial waves, with even and odd parity. They are decoupled if the potential V(x) is symmetric, i.e., V(x)=V(−x). If V(x)≠V(−x), however, the two partial waves are coupled. This coupled-channel problem can be handled in terms of two eigenphases and a mixing parameter. This method enables us to shed new light on the transmission and reflection probabilities at threshold.

DOI
10.1119/1.18123

Related papers

Scattering of relativistic spinless particles within the Feshbach-Villars formalism

YASSINE CHARGUI, A. Dhahbi, A.R. Karam

We consider the relativistic quantum scattering of spinless particles in one-spatial dimension using the Feshbach-Villars formalism. We construct the general form of the scattering matrix, for symmetric and non-symmetric potentials, based on the symmetry properties of the Feshbach-Villars equation. Then, since in one dimension there are only two partial waves associated with even and odd parities, we show, in a simple and comprehensive way, how to describe this transmission-reflection problem using partial-wave decomposition. As an illustration, we also discuss the special case of scattering by a symmetric square-well potential.

Heliyon•Oct 1, 2022•1 citation

Threshold anomalies in one-dimensional scattering

Peter Senn

In one-dimensional scattering, the portion of particles that is transmitted in general vanishes as the kinetic energy of the incident particles approaches zero. Based upon published results from the literature, the present work shows that for a potential consisting of two Dirac δ functions of arbitrary strength, a finite portion of the incident particles is transmitted at threshold for certain choices of the set of parameters defining the potential. The underlying reasons are shown to be related to the structure of the bound levels of the potential. It is shown that for a potential with a finite range but of general shape the reflection coefficient in general tends to unity near threshold, which is what is usually observed. However, in the presence of a bound level at the onset of the continuum, a finite portion of the incident particles is transmitted at threshold for a potential with a general shape and, furthermore, it can be shown that if the potential V is symmetric with V(x)=V(−x) then resonance transmission is observed, i.e., the reflection coefficient vanishes at threshold.

American Journal of Physics•Oct 1, 1988•56 citations

Multiple Reflections in One-Dimensional Quantum Scattering

Wolf Jung

Consider the one-dimensional scattering of an electron from two potentials with non-overlapping supports. We show that the scattering amplitudes can be obtained from those of the single potentials, and these relations can be explained in terms of multiple reflections of partial waves in the region between the two potentials. From http://www.iram.rwth-aachen.de/~jung/, the latest version of this paper is available as jg-97-1.*, and from http://www.ma.utexas.edu/mp arc/, the first version is obtained as 97-659.latex. 1 Introduction The scattering of light by a parallel sheet of glass can be described in terms of the scattering by the front and back surfaces. We show that a similar description is possible for Schrodinger scattering with potentials V 1;2 of compact support, where supp V 1 ae [a; b] is located left of supp V 2 ae [c; d]. Thus the scattering by V = V 1 + V 2 can be understood as a result of multiple reflections between the potentials V 1 and V 2 . The scattering amplitudes...

•Jan 1, 2002•1 citation

Scattering in One Dimension

Rocco Schiavilla

Scattering in one dimension is discussed in terms of wave packets; reflection, transmission, and tunneling probabilities are defined; the WKB method to calculate these probabilities is introduced; the S-matrix for scattering in one dimension is defined; the phase-shift method for one-dimensional parity-invariant potentials is introduced; applications to various combinations of finite and infinite barriers with delta-function potentials are examined.

Cambridge University Press eBooks•Dec 5, 2024•0 citations

One-dimensional multiple scattering in quantum mechanics

Douglas Lessie, Joseph Spadaro

The formal theory of multiple scattering in quantum mechanics is adapted to one dimension and applied to the basic problem of scattering by a double delta-function potential. The multiple scattering method is shown to provide a much more powerful analysis than is obtained by either the one-dimensional partial wave approach or by the standard differential solution to the Schrödinger equation.

American Journal of Physics•Oct 1, 1986•16 citations

Schrödinger transmission through one-dimensional complex potentials

Zafar Ahmed

We prove that for a symmetric complex potential, the probabilities of quantal reflection and transmission of a particle are independent of the direction of incidence of the particle. However, the reflectivity for a nonsymmetric complex potential is found to be sensitive to the direction of incidence of the particle whether it is incident from left or right.

Physical Review A•Sep 1, 2001•77 citations
We study the partial-wave description of scattering of a particle from a one-dimensional potential in quantum mechanics. There are two partial waves, with even and odd parity. They are decoupled if the potential V(x) is symmetric, i.e., V(x)=V(−x). If V(x)≠V(−x), however, the two partial waves are coupled. This coupled-channel problem can be handled in terms of two eigenphases and a mixing parameter. This method enables us to shed new light on the transmission and reflection probabilities at threshold.
We consider the relativistic quantum scattering of spinless particles in one-spatial dimension using the Feshbach-Villars formalism. We construct the general form of the scattering matrix, for symmetric and non-symmetric potentials, based on the symmetry properties of the Feshbach-Villars equation. Then, since in one dimension there are only two partial waves associated with even and odd parities, we show, in a simple and comprehensive way, how to describe this transmission-reflection problem using partial-wave decomposition. As an illustration, we also discuss the special case of scattering by a symmetric square-well potential.
In one-dimensional scattering, the portion of particles that is transmitted in general vanishes as the kinetic energy of the incident particles approaches zero. Based upon published results from the literature, the present work shows that for a potential consisting of two Dirac δ functions of arbitrary strength, a finite portion of the incident particles is transmitted at threshold for certain choices of the set of parameters defining the potential. The underlying reasons are shown to be related to the structure of the bound levels of the potential. It is shown that for a potential with a finite range but of general shape the reflection coefficient in general tends to unity near threshold, which is what is usually observed. However, in the presence of a bound level at the onset of the continuum, a finite portion of the incident particles is transmitted at threshold for a potential with a general shape and, furthermore, it can be shown that if the potential V is symmetric with V(x)=V(−x) then resonance transmission is observed, i.e., the reflection coefficient vanishes at threshold.
Consider the one-dimensional scattering of an electron from two potentials with non-overlapping supports. We show that the scattering amplitudes can be obtained from those of the single potentials, and these relations can be explained in terms of multiple reflections of partial waves in the region between the two potentials. From http://www.iram.rwth-aachen.de/~jung/, the latest version of this paper is available as jg-97-1.*, and from http://www.ma.utexas.edu/mp arc/, the first version is obtained as 97-659.latex. 1 Introduction The scattering of light by a parallel sheet of glass can be described in terms of the scattering by the front and back surfaces. We show that a similar description is possible for Schrodinger scattering with potentials V 1;2 of compact support, where supp V 1 ae [a; b] is located left of supp V 2 ae [c; d]. Thus the scattering by V = V 1 + V 2 can be understood as a result of multiple reflections between the potentials V 1 and V 2 . The scattering amplitudes...