Linear Canonical Transformations and the Hamilton-Jacobi Theory in Quantum Mechanics
Abstract
We investigate two methods of constructing a solution of the Schr\"odinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schr\"odinger 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\"odinger equation.
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