Non-relativistic and relativistic scattering by short-range potentials-Reference-Cited by-同舟云学术

Non-relativistic and relativistic scattering by short-range potentials

Published:2011-03-28 Issue:1939 Volume:369 Page:1228-1244
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Arnbak H.¹,Christiansen P. L.¹²,Gaididei Yu. B.³

Affiliation:

1. Department of Informatics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark

2. Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark

3. Bogolyubov Institute for Theoretical Physics, 03143 Kyiv, Ukraine

Abstract

Relativistic and non-relativistic scattering by short-range potentials is investigated for selected problems. Scattering by the δ ′ potential in the Schrödinger equation and δ potentials in the Dirac equation must be solved by regularization, efficiently carried out by a perturbation technique involving a stretched variable. Asymmetric regularizations yield non-unique scattering coefficients. Resonant penetration through the potentials is found. Approximative Schrödinger equations in the non-relativistic limit are discussed in detail.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2010.0330

Reference14 articles.

1. Method for Solving the Korteweg-deVries Equation

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. Boundary conditions for the states with resonant tunnelling across the -potential

5. Schrödinger operators with singular interactions: a model of tunnelling resonances

Cited by 15 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The physical interpretation of point interactions in one-dimensional relativistic quantum mechanics;Journal of Physics A: Mathematical and Theoretical;2024-02-21

2. Scattering by singular potentials in coupled Schrödinger equations;Low Temperature Physics;2022-12

3. Bound states of a one-dimensional Dirac equation with multiple delta-potentials;Low Temperature Physics;2022-12

4. The general solution for the relativistic and nonrelativistic Schrödinger equation for the δ(n)-function potential in 1-dimension using cutoff regularization, and the fate of universality;International Journal of Modern Physics A;2022-11-20

5. Non-Relativistic Limit for Matrix 1D-Dirac Operators with Point Interactions;Lobachevskii Journal of Mathematics;2022-10