On standing wave solutions to the Schrödinger equation: D.J.Kouri. School of Chemical Sciences, University of Illinois at Urbana-Champagne, Urbana, Illinois 61801, and Department of Chemical Physics, Weizmann Institute of Science, Rehovot, Israel, and F. S. Levin. Department of Physics and Astrophysics, University of Delhi, Delhi 7, India, and Department of Physics, Brown University, Providence, Rhode Island 02912

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 50 KB
• Volume: 82
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(74)90137-7

✦ Synopsis

The standing wave solution to the Schrodinger 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 one-half the sum of the usual ingoing and outgoing wave solutions obeying LippmannSchwinger 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., case & , where Sr 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 6r , since in each case it is the asymptotic ratio of the irregular to the regular solution.