The Morse oscillator in position space, momentum space, and phase space

Jens Peder Dahl, Michael Springborg

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Abstract

We present a unified description of the position-space wave functions, the momentum-space wave functions, and the phase-space Wigner functions for the bound states of a Morse oscillator. By comparing with the functions for the harmonic oscillator the effects of anharmonicity are visualized. Analytical expressions for the wave functions and the phase space functions are given, and it is demonstrated how a numerical problem arising from the summation of an alternating series in evaluating Laguerre functions can be circumvented. The method is applicable also for other problems where Laguerre functions are to be calculated. The wave and phase space functions are displayed in a series of curves and contour diagrams. An Appendix discusses the calculation of the modified Bessel functions of real, positive argument and complex order, which is required for calculating the phase space functions for the Morse oscillator. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
Original languageEnglish
JournalJournal of Chemical Physics
Volume88
Issue number7
Pages (from-to)4535-4547
ISSN0021-9606
DOIs
Publication statusPublished - 1988

Bibliographical note

Copyright (1988) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

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