‘Slow’ time discretization: a versatile time propagator for the time-dependent Schrödinger equation

Abstract

We present the slow time discretization (STD) method for solving the time-dependent Schrödinger equation. The method is an extension of the slow variable discretization method for solving the stationary Schrödinger equation (Tolstikhin et al 1996 J. Phys. B: At. Mol. Opt. Phys. 29 L389), with time treated as the ‘slow’ variable. It is based on an expansion of the state vector in a discrete variable representation basis, in time, and an adiabatic basis, in Hilbert space. This approach is much more efficient in implementation than a direct solution of the Born–Fock equations. The versatility of the STD time propagator is illustrated through calculations for one-dimensional models of the ionization of hydrogen by an intense laser pulse and resonance charge transfer in proton–hydrogen collisions. The method is shown to perform well in the broad dynamical range considered, from adiabatic to nonadiabatic regimes.