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Die S CHRöDINGER ‐Gleichung mit nichtlokalem Potential. I. Die Resolvente
Author(s) -
von der Heydt Nikolaus
Publication year - 1973
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19730290404
Subject(s) - resolvent , physics , bound state , complex plane , schrödinger equation , integral equation , mathematical physics , fredholm integral equation , mathematical analysis , schrödinger's cat , mathematics , quantum mechanics
For a wide class of nonlocal potentials the S CHRÖDINGER integro‐differential equations for the radial waves may be reduced to integral equations containing L 2 ‐kernels. Therefore a number of analytic and functional‐analytic properties of the resolvent of the radial wave equation may be deduced by means of the F REDHOLM method. Thence, the completeness of the physical radial wave functions, among other things, is proved by a known method. The positive‐energy bound states occurring with nonlocal potentials are interpreted as resonances of vanishing width. We consider the non‐imaginary “resonance poles” of the resolvent in a strip 0 > Im k > —α of the complex k ‐plane 1/α being the range of the potential. The structure of the principal parts is specified. The results will be used in the second part of this article.