https://doi.org/10.1007/s100530050185
Expansions for the eigenvalues of three-term recurrence relations. Two applications in molecular physics
1
Laboratoire de Spectrométrie Ionique et
Moléculaire (UMR n° 5579) , CNRS et Université
Lyon I, Bâtiment 205, 43 boulevard du 11 novembre 1918,
69622 Villeurbanne Cedex, France
2
Institut de Physique Nucléaire de Lyon, IN2P3-CNRS, Université
Claude Bernard,
43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
Corresponding author: a frecon@in2p3.fr
Received:
30
January
1998
Revised:
10
April
1998
Accepted:
25
May
1998
Published online: 15 October 1998
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 Schrödinger 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.
PACS: 31. – Electronic structure of atoms, molecules and their ions: theory
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998