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

• Published in: Journal of physics. B, Atomic, molecular, and optical physics Vol. 47; no. 7; pp. 75007 - 9
• Main Authors: Bækhøj, Jens E, Tolstikhin, Oleg I, Madsen, Lars Bojer
• Format: Journal Article
• Language: English
• Published: IOP Publishing 14.04.2014
• Subjects: adiabatic basis; Adiabatic flow; calculations techniques in AMO physics; Discretization; dynamics in atoms and molecules; Lasers; Mathematical analysis; Mathematical models; Representations; Schroedinger equation; State vectors
• ISSN: 0953-4075; 1361-6455
• DOI: 10.1088/0953-4075/47/7/075007

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.