A Note on Semiclassical Bound States and Correspondence Principles.

摘要

Semiclassical bound state theory is considered from the viewpoint of the phase space representations of quantum mechanics. Obtained in the semiclassical limit, within a representation defined by the ordering chosen for the noncommuting position and momentum operators, are (1) equations of motion, which need not be classical and (2) correspondence principles in action-angle variables, regarded as those initial conditions on the equations of motion which dominate in the semiclassical limit. The Weyl ordering is seen to generate the classical equations of motion and the normal correspondence result. Possible evaluation of semiclassical bound state energies is discussed be means of the eigenvalue approach to classical mechanics used by Prigogine and co-workers.