Numerical quantum propagation with time-dependent Hamiltonian

A numerical method was proposed to propagate the quantum system with a time-dependent Hamiltonian. The propagator is composed of the time-independent-Hamiltonian-type multisplit forms, which becomes possible by realizing that the evolution operator has a close link with the time-shift operator. The present algorithm can achieve a high order of accuracy through the recurrence of multisplit forms with predetermined coefficients, and it has the advantage that only the Hamiltonian itself at different time instants is involved, while other currently available schemes need to perform either a time integration or a time differential of the Hamiltonian. This essential difference has made our proposal highly competitive. A one-dimensional model system is considered to verify the accuracy and efficiency of the numerical scheme. (C) 1996 American Institute of Physics.