Using an r-dependent Gaussian width in calculations of the globally uniform semiclassical wave function

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.