Phase-space representation of quantum mechanics and its relation to phase-space path integrals

Publisher Website
Google Scholar
Abstract
A detailed framework for a new formalism of phase-space path integral is presented, the outline of the theory of which has been reported elsewhere [K. Takatsuka, Phys. Rev. Lett. 61, 503 (1988)]. This path integral is described in terms of a phase-space distribution function, which was proposed earlier by the present author under the name of the dynamical characteristic function (DCF). The DCF is characterized by two independent wave functions and with two phase spaces. In the present paper, we extend the DCF by utilizing the Feynman kernel in place of the two independent wave functions. This is called the identity DCF. The dynamics of the DCF for general wave packets is reduced to that of the identity DCF. Some characteristics of the identity DCF are presented. For example, the quantum-mechanical time-evolution operator is represented in terms of the identity DCF and of a complete set of quantum q (coordinate) and p (momentum) operators. A semiclassical theory for the identity DCF is also developed, its primary aim being the study of heavy-particle dynamics such as molecular collisions.

This publication has 25 references indexed in Scilit: