Improved exponential split operator method for solving the time-dependent Schrödinger equation

Abstract

A new method of splitting exponential operators is proposed in the exponential form of the operator solution of the time-dependent Schrödinger equation. The method is shown to be third-order accurate in the time increment. In particular the phase of the wavefunction is shown to be exceptionally accurate for time-independent potentials. The new method is shown to be more efficient than the standard second-order evolution operator algorithms for both time-independent and time-dependent potentials.