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Die SCHRODINGER‐Gleichung mit nichtlokalem Potential. I. Die Resolvente
Author(s) -
von der Heydt N.
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.19734840404
Subject(s) - resolvent , physics , bound state , complex plane , schrödinger equation , mathematical physics , integral equation , fredholm integral equation , mathematical analysis , schrödinger's cat , analytic function , quantum mechanics , mathematics
For a wide class of nonlocal potentials the SCHRÖDINGER 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 FREDHOLM 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.