The Gaussian wave packet transform: Efficient computation of the semi-classical limit of the Schrödinger equation. Part 2. Multidimensional case

A Gaussian wave packet transform is developed for the efficient computation of the semi-classical limit of the multidimensional Schrödinger equation with smooth potential. This transformation, based on Gaussian wave packets, yields a Schrödinger-type equation that is very amenable to numerical solution in the semi-classical limit. The transformed Schrödinger equation is solved with a 4th order splitting method. The wave function can be reconstructed from the transformed wave function whereas some expectation values can easily be evaluated directly. The number of grid points needed per degree of freedom is small enough that computations in dimension of up to 4 or 5 are feasible without the use of any basis thinning procedures.