Nonlocal potentials and their local equivalents: Marcel Coz, Louis G. Arnold, and Alan D. MacKellar. Department of Physics and Astronomy, University of Kentucky, Lexington Kentucky
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 43 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
The transformation of the radial Schrodinger equation for a nonlocal potential to the radial Schrodinger equation for a local potential is investigated. Previous work is clarified and extended to complex values of the wave number. For the purpose of establishing a correspondence between the properties of the nonlocal and local equations, the nonlocal equation is studied in the coordinate representation. In connection with this study, it is shown that the so called spurious state solutions to the nonlocal equation can be attributed to the breakdown of the linear independence of solutions which behave asymptotically as incoming and outgoing waves. The method used to transform the nonlocal equation leads to a unique expression for the equivalent local potential and damping function throughout the domain of definition of the solutions to the nonlocal equation. Both bound states and the continuum are treated by the same method. The transformation is limited by the appearance of the spurious solutions to the nonlocal equation. In the absence of such solutions, the nonlocal and local wave functions have the same phase and the same number of nodes; they differ only by the damping function which is an everywhere positive amplitude factor. For a nonlocal kernel which is real and symmetric, the nonlocal and equivalent local equations have the same spectrum. In this case, the damping function is unity at the origin. The method described is relevant to several problems of current interest.