A fast method for solving both the time-dependent Schrödinger equation in angular coordinates and its associated “m-mixing” problem

Abstract

An efficient split-operator technique for solving the time-dependent Schrödinger equation in an angular coordinate system is presented, where a fast spherical harmonics transform accelerates the conversions between angle and angular momentum representations. Unlike previous techniques, this method features facile inclusion of azimuthal asymmetries (solving the "m-mixing" problem), adaptive time stepping, and favorable scaling, while simultaneously avoiding the need for both kinetic and potential energy matrix elements. Several examples are presented.