Linear Canonical Transformations and the Hamilton-Jacobi Theory in Quantum Mechanics
Quantum Physics
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.quant-ph/0410173,
title = {Linear Canonical Transformations and the Hamilton-Jacobi Theory in Quantum Mechanics},
author = {Akihiro Ogura and Motoo Sekiguchi},
journal= {arXiv preprint arXiv:quant-ph/0410173},
year = {2007}
}