Numerical study of the one-dimensional hydrogen atom in an external time-dependent electric field

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Abstract
A fast and accurate computer code has been developed to solve the Schrödinger equation for the one-dimensional hydrogen atom in an external spatially uniform, time-dependent electric field. Many calculations that previously required hours on a supercomputer can be done in minutes on a workstation. It has been applied to a variety of problems, starting with a system prepared in a hydrogenic eigenstate. In a weak field, for sufficiently short times, the Fermi golden rule has been verified. In very strong fields, the ionization probability oscillates in time, but the mean value increases. Ionization suppression is present only in the averaged sense and with a sudden turnon. For the case of above-threshold ionization, we see ponderomotive shifts and multiphoton resonance peaks in the continuous spectrum. Gauge independence is proved analytically and verified by numerical computations. It is demonstrated that prior numerical work was marred by problems of numerical accuracy and consistency of approximation.