Boundary-free scaling calculation of the time-dependent Schrödinger equation for laser-atom interactions

The time-dependent Schrödinger equation for atoms in an intense laser field is solved in scaled coordinates. Starting with the time propagation of a free particle, we show that scaling removes the spreading and rapid phase variation of a wave packet. By solving the one-dimensional model atom in an intense laser field, we show that stable numerical results are best calculated in the acceleration gauge using scaled coordinates. The wave function thus calculated has the least oscillations and does not spread at large time so that there is no need to introduce absorbers at the boundaries. We show the method is suitable for calculations at any laser field strength. We also show that the scaling method permits propagation to large times thus revealing above threshold ionization structure directly in the wave function.