Nonlocal potentials and their local equivalents

摘要: Abstract The transformation of the radial Schrodinger equation for a nonlocal potential to local is investigated. Previous work clarified and extended complex values wave number. For purpose establishing correspondence between properties equations, studied in coordinate representation. In connection with this study, it shown that so called spurious state solutions can be attributed breakdown linear independence which behave asymptotically as incoming outgoing waves. method used transform leads unique expressions equivalent damping function throughout domain definition equation. Both bound states continuum are treated by same method. limited appearance absence such solutions, functions have phase number nodes; they differ only an everywhere positive amplitude factor. kernel real symmetric, equations spectrum, case, unity at origin. described relevant several problems current interest.