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 propa gating a wave function, rather than evolving in time the Feynman kerne l, is presented. It turns out that the present solution bears distingu ished advantages over the semiclassical kernel, one of the most remark able examples of which is the far less number of classical trajectorie s required for the propagation, basically proportional to p(2N) simila r to p(3N) for the kernel while only to P-N in our solution, where N i s the dimension in configuration space and P is the number of sampling points in each dimension. As an illustrative example to show the vali dity of the solution, the theory is applied to the calculation of eige nvalues of the Morse oscillators, giving accurate results in a compact way.