Ionization of atoms by strong infrared fields: Solution of the time-dependent Schrodinger equation in momentum space for a model based on separable potentials

We consider the ionization of atomic hydrogen by a strong infrared field. By starting from the corresponding time-dependent Schrodinger equation in momentum space, we develop a model in which the kernel of the nonlocal Coulomb potential is replaced by a finite sum of separable potentials. Each separable potential supports one bound state of atomic hydrogen. Here, we consider only the 1s, 2s, and 2p states. In this way, the full three-dimensional Schrodinger equation reduces to a system of a few coupled one-dimensional linear Volterra integral equations. The objective of this first contribution is to give a detailed account of the model and to validate it in physical situations where the dynamics are well understood.