  We present results on the accurate one-dimensional (1D) modeling of simple
atomic and molecular systems excited by strong laser fields. We use atomic
model potentials that we derive from the corrections proposed earlier using the
reduced ground state density of a three-dimensional (3D) single-active electron
atom. The correction involves a change of the asymptotics of the 1D Coulomb
model potentials while maintaining the correct ground state energy. We present
three different applications of this method: we construct correct 1D models of
the hydrogen molecular ion, the helium atom and the hydrogen molecule using
improved parameters of existing soft-core Coulomb potential forms. We test
these 1D models by comparing the corresponding numerical simulation results
with their 3D counterparts in typical strong-field physics scenarios with near-
and mid-infrared laser pulses, having peak intensities in the
$10^{14}-10^{15}\,\mathrm{W/cm}^2$ range, and we find an impressively increased
accuracy in the dynamics of the most important atomic quantities on the time
scale of the excitation. We also present the high-order harmonic spectra of the
He atom, computed using our 1D atomic model potentials. They show a very good
match with the structure and phase obtained from the 3D simulations in an
experimentally important range of excitation amplitudes.
