Linear Canonical Transformations and the Hamilton-Jacobi Theory in   Quantum Mechanics
  We investigate two methods of constructing a solution of the Schr\"{o}dinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schr\"{o}dinger equation from linear canonical transformations, the other focuses on the generating function which satisfies the Hamilton-Jacobi equation in classical mechanics. We also show that these two methods lead to the same solution of the Schr\"{o}dinger equation. 
Akihiro Ogura and Motoo Sekiguchi