scholarly journals A transmutation operator method for solving the inverse quantum scattering problem

2020 ◽  
Vol 36 (12) ◽  
pp. 125007
Author(s):  
Vladislav V Kravchenko ◽  
Elina L Shishkina ◽  
Sergii M Torba
Keyword(s):  
Scattering Problem ◽  
Operator Method ◽  
Quantum Scattering ◽  
Transmutation Operator

Topological quantum scattering under the influence of a nontrivial boundary condition

2016 ◽  
Vol 31 (11) ◽  
pp. 1650074 ◽  
Author(s):  
Herondy Mota
Keyword(s):  
Boundary Condition ◽  
Phase Shift ◽  
Gordon Equation ◽  
Scattering Problem ◽  
Quantum Scattering ◽  
Topological Quantum ◽  
Klein Gordon ◽  
Bohm Effect ◽  
Aharonov Bohm

We consider the quantum scattering problem of a relativistic particle in (2 + 1)-dimensional cosmic string spacetime under the influence of a nontrivial boundary condition imposed on the solution of the Klein–Gordon equation. The solution is then shifted as consequence of the nontrivial boundary condition and the role of the phase shift is to produce an Aharonov–Bohm-like effect. We examine the connection between this phase shift and the electromagnetic and gravitational analogous of the Aharonov–Bohm effect and compare the present results with previous ones obtained in the literature, also considering non-relativistic cases.

scholarly journals Nonrelativistic Charged Particle-Magnetic Monopole Scattering in the Global Monopole Background

2003 ◽  
Vol 18 (18) ◽  
pp. 3175-3187 ◽  
Author(s):  
A. L. Cavalcanti de Oliveira ◽  
E. R. Bezerra de Mello
Keyword(s):  
Charged Particle ◽  
Energy Spectrum ◽  
Magnetic Monopole ◽  
Scattering Problem ◽  
Quantum Scattering ◽  
Global Monopole ◽  
Nonrelativistic Quantum ◽  
Geometric Effects

We analyze the nonrelativistic quantum scattering problem of a charged particle by an Abelian magnetic monopole in the background of a global monopole. In addition to the magnetic and geometric effects, we consider the influence of the electrostatic self-interaction on the charged particle. Moreover, for the specific case where the electrostatic self-interaction becomes attractive, the charged particle-monopole bound system can be formed and the respective energy spectrum is a hydrogen-like one.

Quantum inversion with elastic phase shifts to discrete different energies

2014 ◽  
Vol 23 (11) ◽  
pp. 1450077
Author(s):  
Werner Scheid ◽  
Barnabas Apagyi
Keyword(s):  
Angular Momentum ◽  
Elastic Scattering ◽  
Nuclear Physics ◽  
Scattering Problem ◽  
Phase Shifts ◽  
The Other ◽  
Quantum Scattering ◽  
Fixed Energy ◽  
Correct Energy ◽  
Radial Potential

We consider the inverse quantum scattering problem with phase shifts of different discrete energies belonging to a real energy-independent radial potential for elastic scattering. The solution of this problem is essential for atomic and nuclear physics. The two procedures investigated are based on the modified Newton–Sabatier method. The first procedure leads to angular-momentum dependent potentials with poles. The second one carries out an inversion at a fixed energy by varying the phase shifts of the other energies and leads finally to the correct energy-independent potential.

SOLUTION OF THE INVERSE SCATTERING PROBLEM AT FIXED ENERGY FOR POTENTIALS BEING ZERO BEYOND A FIXED RADIUS

2008 ◽  
Vol 22 (23) ◽  
pp. 2137-2149 ◽  
Author(s):  
MIKLÓS HORVÁTH ◽  
BARNABÁS APAGYI
Keyword(s):  
Integral Equation ◽  
Bound States ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Quantum Scattering ◽  
Minimum Norm ◽  
Fixed Energy ◽  
Scattering Phase ◽  
Fixed Radius ◽  
Scattering Phase Shifts

Based on the relation between the m-function and the spectral function we construct an inverse quantum scattering procedure at fixed energy which can be applied to spherical radial potentials vanishing beyond a fixed radius a. To solve the Gelfand–Levitan–Marchenko integral equation for the transformation kernel, we determine the input symmetrical kernel by using a minimum norm method with moments defined by the input set of scattering phase shifts. The method applied to the box and Gauss potentials needs further practical developments regarding the treatment of bound states.

scholarly journals The Physics of Low-energy Electron-Molecule Collisions: A Guide for the Perplexed and the Uninitiated

1983 ◽  
Vol 36 (3) ◽  
pp. 239 ◽  
Author(s):  
Michael A Morrison
Keyword(s):  
Vibrational Excitation ◽  
Scattering Problem ◽  
Low Energy ◽  
Energy Electron ◽  
Quantum Scattering ◽  
Physical Interactions ◽  
Low Energy Electron ◽  
Frame Transformation ◽  
Molecule Scattering ◽  
Physical Features

The essential physical features of low-energy electron-molecule scattering are described in a qualitative fashion. The context for this discussion is provided by the frame-transformation picture, which entails a 'partitioning' of the quantum scattering problem according to the relative importance of various physical interactions. This picture is then used as the basis for a qualitative overview of several contemporary theoretical techniques for solving the quantum scattering problem that are based on eigenfunction expansions of the system wavefunction and for representing the electronmolecule interaction potential. Finally, progress in three specific problem areas of recent interest is surveyed. The emphasis throughout is on non-resonant elastic scattering and ro-vibrational excitation.

scholarly journals Variable phase equation in quantum scattering

2014 ◽  
Vol 36 (1) ◽  
Author(s):  
Vitor D. Viterbo ◽  
Nelson H.T. Lemes ◽  
João P. Braga
Keyword(s):  
Differential Equation ◽  
Angular Momentum ◽  
Order Differential Equation ◽  
Single Channel ◽  
Scattering Problem ◽  
Quantum Scattering ◽  
Phase Equation ◽  
Variable Phase ◽  
First Order ◽  
Levinson’S Theorem

This paper presents the derivation and applications of the variable phase equation for single channel quantum scattering. The approach was first presented in 1933 by Morse and Allis and is based on a modification of the Schrödinger equation to a first order differential equation, appropriate to the scattering problem. The dependence of phase shift on angular momentum and energy, together with Levinson's theorem, is discussed. Because the variable phase equation method is easy to program it can be further explored in an introductory quantum mechanics course.

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