title: Using an r-dependent Gaussian width in calculations of the globally uniform semiclassical wave function.
abstract: The globally uniform semiclassical wave function expresses the solution to the time independent Schrodinger equation in terms of fixed width Gaussian wave packets traveling along a set of trajectories. There is a globally uniform wave function (GUWF) for each value of the Gaussian width parameter gamma. Numerical data show that a small Gaussian width is needed in some regions to obtain accurate results, while a broad Gaussian width provides better results in other regions. Since there is a semiclassically valid GUWF for every positive value of gamma, it is reasonable to employ the GUWF corresponding to a Gaussian width that provides good results at each value of r. A criterion for the r dependent choice of gamma is proposed and tested on one and two dimensional model problems. The results show that the use of an r dependent gamma in the GUWF results in improved accuracy for the model problems considered.
authors.affiliation: Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA.
authors.forename: Michael F
authors.initials: MF
authors.lastname: Herman
authors.forename: Alexey
authors.initials: A
authors.lastname: Sergeev