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Quantum mechanical scattering theory for potentials of the form *V*(*r*) = (sin *r*)/*r* ^{ β} , 1/3<β≤1/2

### Abstract

A rigorous nonrelativistic time dependent quantum‐mechanical scattering theory for a single particle is developed for potentials of the form *V*(*r*) = (sin *r*)/*r* ^{ β} , 1/3<β⩽ 1/2 . The positive‐energy solutions of the radial Schrödinger equation are used to construct modified wave operators which converge as *t*→±∞ on a dense set of states to the familiar time‐independent formulas for the wave operators.

© 1982 American Institute of Physics

/content/aip/journal/jmp/23/5/10.1063/1.525418

http://aip.metastore.ingenta.com/content/aip/journal/jmp/23/5/10.1063/1.525418

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