title: Quantum Hamilton-Jacobi theory.
abstract: Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear operator partial differential equation such as the quantum Hamilton-Jacobi equation (QHJE) has hindered progress along this otherwise promising avenue. We overcome this difficulty. We show that solutions to the QHJE can be constructed by a simple prescription starting from the propagator of the associated Schrödinger equation. Our result opens the possibility of practical use of quantum Hamilton-Jacobi theory. As an application, we develop a surprising relation between operator ordering and the density of paths around a semiclassical trajectory.
authors.affiliation: INFN, Sezione di Pavia, Via A. Bassi 6, I-27100 Pavia, Italy. marco.roncadelli@pv.infn.it
authors.forename: Marco
authors.initials: M
authors.lastname: Roncadelli
authors.forename: L S
authors.initials: LS
authors.lastname: Schulman