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Franck–condon factors and ladder operators. I. harmonic oscillator
Author(s) -
Palma A.,
Morales J.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560240843
Subject(s) - harmonic oscillator , anharmonicity , harmonic , physics , atomic physics , quantum mechanics
Recurrence relations and closed formulas for the calculation of Franck–Condon factors of harmonic oscillator wave functions have been derived by several authors. The most useful relations are those of Ansbacher. His derivation makes explicit use of the unwieldy Hermite polynomials and its integral representation. We present in this work a rederivation of Ansbacher recurrence relations. This one is based on the algebraic properties of the ladder operators of the harmonic oscillator. The method, which is elegant and simple, leads, in addition, to the general formula for two displaced oscillators with different frequencies. Several particular cases are treated and closed expressions are given.