Remarks on semiclassical quantization

Abstract

Semiclassical quantization in the basic, or ‘‘primitive,’’ version often predicts a simpler, more highly degenerate energy level spectrum than is observed. This point is illustrated by remarks on two‐dimensional systems with threefold and higher rotational symmetry and on perturbations of such systems. For example, according to semiclassical quantization essentially all energy levels of a C₃ system are at least doubly degenerate. Such ‘‘incorrect’’ degeneracy predictions are to be interpreted as predictions of coalescence of levels in the semiclassical (ℏ→0) limit, coalescence which may manifest itself in real spectra as an excess of near degeneracies. Finally, a consideration on degeneracy rules out one possible solution to the problem of semiclassical quantization of ergodic systems.