L. Sirko et Pm. Koch, THE PENDULUM APPROXIMATION FOR THE MAIN QUANTAL RESONANCE ZONE IN PERIODICALLY DRIVEN HYDROGEN-ATOMS, Applied physics. B, Lasers and optics, 60(2-3), 1995, pp. 195-202
We review the quasienergy level structure of sinusoidally driven 1d hy
drogen atoms close to the main classical nonlinear resonance zone. In
the near-resonant-state approximation, this becomes the problem of the
quantal pendulum, whose eigensolutions are those of a Mathieu equatio
n. We test the accuracy of the approximate quasi-energies obtained fro
m the pendulum solutions by comparing them to more accurate numerical
Floquet calculations. We show that the number of (atom + field) states
whose quasi-energies are approximated accurately by the pendulum eige
nsolutions corresponds well with the phase-space area (measured in uni
ts of Planck's quantum of action h) within the separatrix of the class
ical nonlinear resonance zone.