Scattering by singular potentials in coupled Schrödinger equations-Reference-Cited by-同舟云学术

Scattering by singular potentials in coupled Schrödinger equations

Published:2022-12 Issue:12 Volume:48 Page:1033-1037
ISSN:1063-777X
Container-title:Low Temperature Physics
language:en
Short-container-title:Low Temperature Physics

Author:

Christiansen Peter L.¹,Rasmussen Jens Juul²,Sørensen Mads Peter³^ORCID

Affiliation:

1. Department of Applied Mathematics and Computer Science and Department of Physics Technical University of Denmark, DK−2800 Kgs. Lyngby, Denmark

2. Department of Physics, Technical University of Denmark, DK−2800 Kgs. Lyngby, Denmark

3. Department of Applied Mathematics and Computer Science, Technical University of Denmark DK−2800 Kgs. Lyngby, Denmark

Abstract

Scattering in pairs of one-dimensional time-independent Schrödinger equations coupled via singular potentials are considered. For potentials given by Dirac’s delta function reflected and transmitted waves of the two modes as well as a bound state is found by integration. For potentials given by the derivative of Dirac’s delta function, resonant reflection and transmission occur for a discrete set of amplitudes of the scattering potential. These results depend on the applied regularization.

Publisher

AIP Publishing

Subject

General Physics and Astronomy,Physics and Astronomy (miscellaneous)

Link

https://aip.scitation.org/doi/pdf/10.1063/10.0015112

Reference11 articles.

1. Schrödinger equation with δ' and δ" potentials

2. On the existence of resonances in the transmission probability for interactions arising from derivatives of Dirac s delta function

3. Scattering properties of point dipole interactions

4. Transmission–reflection problem with a potential of the form of the derivative of the delta function

5. Alexander V. Zolotaryuk and Yaroslav Zolotaryuk, “Existence of a Bound State for the λδ′(x) potential,” Yuri Gaididei Memorial Workshop, February 2–3, 2022, Kyiv, Ukraine, unpublished.