THE PENDULUM APPROXIMATION FOR THE MAIN QUANTAL RESONANCE ZONE IN PERIODICALLY DRIVEN HYDROGEN-ATOMS

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.