Semiclassical Trajectory-Coherent Approximation in Quantum Mechanics I. High-Order Corrections to Multidimensional Time-Dependent Equations of Schrödinger Type

Abstract

A concept of semiclassically concentrated states is developed on the basis of the Maslov germ theory. Higher approximations of semiclassical trajectory-coherent states and of semiclassical Green function (in the class of semiclassically concentrated states) for a many-dimensional Schrödinger-type equation are constructed. It is shown that, in class of such semiclassically concentrated states, a Schrödinger-type equation (up to any order of ℏ, ℏ→0) is equivalent, from the viewpoint of calculating the quantum averages, to a closed finite system of ordinary differential equations.