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

doi:https://doi.org/10.1103/PhysRevD.13.913

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

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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:: Pattanayak, D N; Wolf, W

Publication Date:: 1976-02-15

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

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                    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.

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                    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

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                    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.

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@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}

}

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