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On standing wave solutions to the Schrödinger equation

✍ Scribed by D.J Kouri; F.S Levin

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
437 KB
Volume
83
Category
Article
ISSN
0003-4916

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✦ Synopsis

The standing wave solution to the Schriidinger equation defined in terms of the standing wave Green's function for the full Hamiltonian is discussed. This solution is compared with the more usual standing wave solution. The former is shown to be onehalf the sum of the usual ingoing and outgoing wave solutions obeying Lippmann-Schwinger equations. Partial wave elements of the two solutions as well as of the two reaction (K) matrices are found to be related by a simple normalization factor, viz. co? 6, ) where 6, is the Ith partial wave phase shift. Thus, either of the two standing wave solutions can be used to obtain the correct K matrix element, tan 6, , since in each case it is the asymptotic ratio of the irregular to the regular solution.

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