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

Resonance scattering from a double δ-function potential

I. Richard Lapidus

Published Jul 1, 1982• 13 citations
Publisher

Abstract

The transmission coefficient and total cross section as functions of energy are obtained for scattering of particles by a double δ-function potential in one dimension. This example may be useful for the discussion of resonance scattering in an introductory quantum mechanics course. (AIP)
DOI
10.1119/1.12780

Related papers

Quantum Theory of a Square Well Plus Delta Function Potential

W. Edward Gettys

The s-wave Schrödinger equation is solved for a square well potential with an attractive delta function at the well edge. This potential provides a number of soluble illustrations of the techniques of quantum mechanics. The bound state eigenvalue problem is solved as is the scattering problem for the cross section. The potential is capable of producing a sharp low energy resonance. The resonances are discussed using both R-matrix and S-matrix methods. Numerical examples are presented.

American Journal of Physics•May 1, 1973•2 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

Scattering by two-dimensional circular barrier, hard circle, and delta function ring potentials

I. Richard Lapidus

Scattering lengths are obtained for the scattering of particles from two-dimensional circular barrier, hard circle, and delta function ring potentials using classical mechanics and quantum mechanics. These results will be of interest in a quantum mechanics course as a supplement to the discussion of three-dimensional scattering.

American Journal of Physics•May 1, 1986•24 citations

Repulsive Delta-Function Potential in Two and Three Dimensions

Minoru Takahashi

It is shown by choosing an appropriate variational wave function that the ground state energy is not affected by the repulsive delta-function potential in two and three dimensional systems. Scattering cross section by the repulsive delta-function potential is shown to be zero.

Journal of the Physical Society of Japan•Mar 1, 1982•1 citation

Scattering from an attractive delta-function potential

Clinton DeW. Van Siclen

A one−dimensional calculation is carried out to determine the phase shifts for scattering from an attractive delta−function potential. (AIP)

American Journal of Physics•Mar 1, 1988•10 citations

Quadrupolar, triple δ-function potential in one dimension

S. H. Patil

The energy and parity eigenstates for quadrupolar, triple δ-function potential are analysed. Using the analytical solutions in specific domains, simple expressions are obtained for even- and odd-parity bound-state energies. The Heisenberg uncertainty product is observed to have a minimum for a specific strength of the potential. The scattering states have a transmission resonance for some energies, and the poles of the transmission coefficients correspond to bound-state energies. These features are of considerable pedagogical interest in the understanding of quantum-mechanical properties of bound and scattering states, for graduate and general physicists.

European Journal of Physics•Apr 9, 2009•7 citations
The energy and parity eigenstates for quadrupolar, triple δ-function potential are analysed. Using the analytical solutions in specific domains, simple expressions are obtained for even- and odd-parity bound-state energies. The Heisenberg uncertainty product is observed to have a minimum for a specific strength of the potential. The scattering states have a transmission resonance for some energies, and the poles of the transmission coefficients correspond to bound-state energies. These features are of considerable pedagogical interest in the understanding of quantum-mechanical properties of bound and scattering states, for graduate and general physicists.