SEMICLASSICAL MECHANICS IN ONE-DIMENSION - II - APPROXIMATE MATRIX-ELEMENTS

The semiclassical formula for matrix elements, sometimes called the He isenberg correspondence principle, relates matrix elements (operators in energy representation) to phase space functions (Weyl representativ es). The formula does not make sense for arbitrary operators; when it is valid it implicitly fixes the relative phases of the eigenfunctions of the Hamiltonian. The conventions, which have to be used for the wa vefunctions in position or momentum representation, are given here in explicit form, and we present a class of operators related to coherent states of high energy for which the Heisenberg correspondence princip le holds.