Correspondence identities: I

Abstract

The complete quantum-dynamical solutions for a free particle moving in one dimension and for a free particle moving on a ring are obtained in terms of classical path sums. The propagators and Green operator kernels, and, in particular, the kernel of the spectral operator I_E = δ(E - H) are expressed explicitly in this way. Relations between quantum and classical mechanics which hold for low quantum numbers and relatively small values of the classical action are discussed. They are the correspondence identities.