Nonlinear resonance in the hydrogen atom

A theoretical and computational analysis in both classical and quantum mechanics demonstrates the existence of nonlinear resonance zones in the 1-dimensional approximation for extreme Stark states of hydrogen perturbed by a microwave field. Comparison of simulations in the "physical" phase space with Koch's laboratory results provide the first explanation of the widths of his regions of suppressed ionization in terms of the expansion of nonlinear resonance zones. It is also confirmed that the locations of the said regions are predicted with great precision in terms of resonance zones.; Also included is the first demonstration of the existence of resonance zones in the quantum mechanical Hilbert space, and the overlap of the zones in a manner exactly analogous to the classical behavior.