Semiclassical integrable matrix elements.

Abstract

A semiclassical expression for matrix elements of an arbitrary operator with respect to the eigenstates of an integrable Hamiltonian is derived. This is essentially the Heisenberg correspondence principle, and it is shown via the Weyl correspondence that the approximation is valid through the lowest two orders in \ensuremath{\Elzxh}. The result is used to prove that an asymptotic form of the Clebsch-Gordan coefficients for two large and one small angular momenta is valid through two orders. \textcopyright{} 1996 The American Physical Society.