Global Representation of Maslov-Type Semiclassical Wave Function and Its Spectrum in a Small Number of Classical Trajectories

An explicit solution to the Maslov-type semiclassical theory for propagating a wave function, rather than evolving in time the Feynman kernel, is presented. It turns out that the present solution bears distinguished advantages over the semiclassical kernel, one of the most remarkable examples of which is the far less number of classical trajectories required for the propagation, basically proportional to P2N∼P3N for the kernel while only to PN in our solution, where N is the dimension in configuration space and P is the number of sampling points in each dimension. As an illustrative example to show the validity of the solution, the theory is applied to the calculation of eigenvalues of the Morse oscillators, giving accurate results in a compact way. copyright 1997 The American Physical Society