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On the validity of the strong field approximation and simple man's theory

Few-cycle above-threshold ionization spectra of atomic hydrogen, calculated via the numerical solution of the time-dependent Schrödinger equation (TDSE), are compared with those predicted by the strong field approximation. Good agreement is obtained for the energetic, rescattered photoelectrons whereas the low-energy part of the electron spectra differ significantly. The latter disagreement is shown to originate from the long-range character of the Coulomb potential. In the second part of the paper a novel quantum distribution function is introduced, which facilitates a direct comparison of the classical electron orbits used in simple man's theory with the exact numerical TDSE result. It is shown that well localized electron wave packets emerge, oriented along the simple man's classical trajectories as the energy resolution in the quantum distribution function is reduced.