Spectral fitting method for the solution of time-dependent Schrödinger equations: Applications to atoms in intense laser fields

Abstract

A spectral fitting method for solving the time-dependent Schr\"odinger equation has been developed and applied to the atom in intense laser fields. This method allows us to obtain a highly accurate time-dependent wave function with a contribution from the high-order term of $▵t.$ Moreover, the time-dependent wave function is determined on a small number of discrete mesh points, thus making calculations simple and accurate. This method is illustrated by computing wave functions and harmonic generation spectra of a model atom in laser fields.