The globally uniform semiclassical wave function expresses the solution to the time independent Schrödinger 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 γ. 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 γ, 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 γ is proposed and tested on one and two dimensional model problems. The results show that the use of an r dependent γ in the GUWF results in improved accuracy for the model problems considered.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics