Expansions for the eigenvalues of three-term recurrence relations. Two applications in molecular physics |
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| Authors: | G. Hadinger M. Aubert-Frécon G. Hadinger |
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| Affiliation: | (1) Laboratoire de Spectrométrie Ionique et Moléculaire (UMR no 5579), CNRS et Université Lyon I, Batiment 205, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France, FR;(2) Institut de Physique Nucléaire de Lyon, IN2P3-CNRS, Université Claude Bernard, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France, FR |
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| Abstract: | Approximate expressions for the eigenvalue of a three-term recurrence relation with a general form describing various physical problems are proposed. Their range of availability is examined by comparison with exact values for two different problems: the bound and continuum states of monoelectronic diatomic ions and the Schr?dinger equation describing molecular alignment in intense laser fields. For each case, very good predictions have been obtained, which may be useful as initial values in iterative procedures for deriving exact solutions. Received: 30 January 1998 / Received in final form: 10 April 1998 / Accepted: 25 May 1998 |
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| Keywords: | PACS. 31. Electronic structure of atoms molecules and their ions: theory |
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