Abstract
A variational principle for the time-dependent Schr\"odinger equation with an anisotropic Gaussian wave packet as a trial wave function is used to calculate the nonperturbative response of a hydrogen atom to a strong linearly polarized laser field. This method leads to equations of motion for the position expectation value and allows one to study a classical (\ensuremath{\Elzxh}=0) limit as well as the first quantum corrections. These corrections are shown to be responsible for a strong enhancement in the generation of the third and fifth harmonic by the bound-state part of the electronic wave function for field intensities of the order of ${10}^{14}$ W/${\mathrm{cm}}^{2}$ and a laser frequency corresponding to three-photon ionization. For a low-frequency field a strong nonperturbative enhancement of harmonics of orders 9 to 15 is observed. It is concluded that the plateau at even higher harmonics observed recently in experiment and in numerical calculations is caused by the ionizing parts of the wave function that are not represented in the present calculation.
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