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Published Online: 31 August 1998
Accepted: December 1987

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

J. Chem. Phys. 88, 4535 (1988); https://doi.org/10.1063/1.453761
Jens Peder Dahl
  • Chemical Physics, Chemistry Department B, Technical University of Denmark, DTH 301, DK‐2800 Lyngby, Denmark
    • Michael Springborg
  • Nordisk Institut for Teoretisk Atomfysik (NORDITA), Blegdamsvej 17, DK‐2100 Ko/benhavn O/, Denmark
    • more...
    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.

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