  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
Schroedinger 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.
