SEMICLASSICAL TRAJECTORY-COHERENT APPROXIMATION IN QUANTUM-MECHANICS .1. HIGH-ORDER CORRECTIONS TO MULTIDIMENSIONAL TIME-DEPENDENT EQUATIONS OF SCHRODINGER TYPE

A concept of semiclassically concentrated states is developed on the b asis of the Maslov germ theory. Higher approximations of semiclassical trajectory-coherent states and of semiclassical Green function (in th e class of semiclassically concentrated slates) for a many-dimensional Schrodinger-type equation are constructed. It is shown that, in class of such semiclassically concentrated states, a Schrodinger-type equat ion (up to any order of h, h --> 0) is equivalent, from the viewpoint of calculating the quantum averages, to a closed finite system of ordi nary differential equations. (C) 1996 Academic Press, Inc.