Scattering states and bound states as solutions of the Schrodinger equation with nonlocal boundary conditions
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)
- Research Organization:
- Department of Physics, University of Toronto, Toronto M5S 1A7 Canada
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-33-032028
- OSTI ID:
- 4009009
- Journal Information:
- Phys. Rev., D, v. 13, no. 4, pp. 913-923, Other Information: Orig. Receipt Date: 30-JUN-76
- Country of Publication:
- United States
- Language:
- English
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