Ke. Thylwe et F. Bensch, NARROW-TUBE APPROXIMATION OF SEMICLASSICAL QUASI-ENERGIES - APPLICATION TO THE WEAKLY NONLINEAR DUFFING OSCILLATOR, Journal of physics. A, mathematical and general, 27(16), 1994, pp. 5673-5685
An exact transformation of semiclassical quantization conditions deter
mining quantal quasi-energies of time-periodic Hamiltonian systems is
suggested. For motion on vortex tubes centred at stable periodic orbit
s the classical quasi-energy of the underlying periodic orbit separate
s out as a single term which is a lower bound for the quantized quasi-
energies. A particular approximation involving the classical Lewis inv
ariant for calculating semiclassical quasi-energies near the centre of
a perturbed linear response is discussed in some detail.