Mapping the Wigner distribution function of the Morse oscillator onto a semiclassical distribution function
Abstract
The mapping of the Wigner distribution function (WDF) for a given bound state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse oscillator. The purpose of the present work is to obtain values of the potential parameters represented by the number of levels in the case of the Morse oscillator, for which the SDF becomes a faithful approximation of the corresponding WDF. We find that for a Morse oscillator with one level only, the agreement between the WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it becomes satisfactory. We also discuss the limit planck rarr 0 for fixed potential parameters.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 2004
 DOI:
 10.1088/03054470/37/11/010
 arXiv:
 arXiv:quantph/0304092
 Bibcode:
 2004JPhA...37.3687B
 Keywords:

 Quantum Physics
 EPrint:
 Revtex, 27 pages including 13 eps figures