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We give a dynamical explanation for the localization of the wave function for the one-dimensional hydrogen atom, with the Coulomb singularity, in a high-frequency electric field, which leads to a necessary condition for classical dynamics to be valid. Numerical tests confirm the accuracy of the condition. Our analysis is relevant to the comparison between the classical and quantal dynamics of the kicked rotor and standard map.
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Leopold et al. (1988) studied this question.
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