P. Kasperkovitz et M. Peev, SEMICLASSICAL MECHANICS OF PERIODIC MOTION - I - GENERAL SCHEME, Journal of physics. A, mathematical and general, 31(9), 1998, pp. 2197-2225
A unified treatment of quantum mechanical oscillatory motion in one di
mension is presented in a phase space formalism which is especially ad
apted to the semiclassical energy domain and closely related to a 'nai
ve' quantization of action and angle variables. Characteristics of thi
s scheme are non-classical symmetry properties of the phase space func
tions representing density operators and observables and the inclusion
of half-Bohr orbits besides the familiar Bohr orbits. Over long time
intervals the quantum evolution can be well approximated by a Hamilton
ian flow along these distinguished classical orbits. The interplay of
this reduced classical evolution and the symmetry properties of the ph
ase space functions results in a consistent quantitative description o
f quantum interference effects which are most clearly seen in the revi
vals of wavepackets.