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Title: Scattering states and bound states as solutions of the Schrodinger equation with nonlocal boundary conditions

Abstract

The problem of determining the Schrodinger wave function of a nonrelativistic particle that is either scattered by a potential of a finite range or that is bound to it is reformulated in a novel way. It is shown that in either case the wave function must satisfy a certain boundary condition on the surface that delimits the effective range of the potential. For scattering states the boundary condition is analogous to the mathematical formulation of the Ewald-Oseen extinction theorem of classical electromagnetic theory. The new formulation is illustrated by determining the scattering states and the bound states for a central potential. It is also shown that a boundary condition that is used in band-structure calculations in solids is an immediate consequence of our quantum-mechanical extinction theorem for bound states. (AIP)

Authors:
;
Publication Date:
Research Org.:
Department of Physics, University of Toronto, Toronto M5S 1A7 Canada
Sponsoring Org.:
USDOE
OSTI Identifier:
4009009
NSA Number:
NSA-33-032028
Resource Type:
Journal Article
Journal Name:
Phys. Rev., D, v. 13, no. 4, pp. 913-923
Additional Journal Information:
Other Information: Orig. Receipt Date: 30-JUN-76
Country of Publication:
United States
Language:
English
Subject:
N76100* -Physics (Theoretical)-General; 644001*; *SCHROEDINGER EQUATION- SCATTERING; BOUNDARY CONDITIONS; EIGENFUNCTIONS; FINITE-RANGE INTERACTIONS; QUANTUM MECHANICS; WAVE FUNCTIONS

Citation Formats

Pattanayak, D N, and Wolf, W. Scattering states and bound states as solutions of the Schrodinger equation with nonlocal boundary conditions. United States: N. p., 1976. Web. doi:10.1103/PhysRevD.13.913.
Pattanayak, D N, & Wolf, W. Scattering states and bound states as solutions of the Schrodinger equation with nonlocal boundary conditions. United States. https://doi.org/10.1103/PhysRevD.13.913
Pattanayak, D N, and Wolf, W. Sun . "Scattering states and bound states as solutions of the Schrodinger equation with nonlocal boundary conditions". United States. https://doi.org/10.1103/PhysRevD.13.913.
@article{osti_4009009,
title = {Scattering states and bound states as solutions of the Schrodinger equation with nonlocal boundary conditions},
author = {Pattanayak, D N and Wolf, W},
abstractNote = {The problem of determining the Schrodinger wave function of a nonrelativistic particle that is either scattered by a potential of a finite range or that is bound to it is reformulated in a novel way. It is shown that in either case the wave function must satisfy a certain boundary condition on the surface that delimits the effective range of the potential. For scattering states the boundary condition is analogous to the mathematical formulation of the Ewald-Oseen extinction theorem of classical electromagnetic theory. The new formulation is illustrated by determining the scattering states and the bound states for a central potential. It is also shown that a boundary condition that is used in band-structure calculations in solids is an immediate consequence of our quantum-mechanical extinction theorem for bound states. (AIP)},
doi = {10.1103/PhysRevD.13.913},
url = {https://www.osti.gov/biblio/4009009}, journal = {Phys. Rev., D, v. 13, no. 4, pp. 913-923},
number = ,
volume = ,
place = {United States},
year = {1976},
month = {2}
}