The Morse oscillator in position space, momentum space, and phase space
Abstract
We present a unified description of the positionspace wave functions, the momentumspace wave functions, and the phasespace 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.
 Publication:

Journal of Chemical Physics
 Pub Date:
 April 1988
 DOI:
 10.1063/1.453761
 Bibcode:
 1988JChPh..88.4535D