| Quantum canonical transformations have attracted interest since the early days of quantum mechanics and one would expect them to provide a powerful tool to solve quantum-mechanical problems much in the same way as it happens in classical mechanics. However, the difficulty of solving a nonlinear operator partial differential equation such as the quantum Hamilton-Jacobi equation (QHJE) has hindered progress along this avenue. It is shown how this difficulty can be overcome. Basically, the knowledge of the Schroedinger propagator allows to construct a complete solution to the QHJE. A few applications of this result will be discussed. |
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