Remarks on semiclassical quantization

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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.

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