Linear Canonical Transformations and the Hamilton-Jacobi Theory in Quantum Mechanics

2004/10/22 by Akihiro Ogura, Ogura, Akihiro, Motoo Sekiguchi +1
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0410173

arxiv created 2004/10/22 · openalex publication_date 2004/10/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate two methods of constructing a solution of the Schrödinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schrödinger 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 Schrödinger equation.

Citations

• Space-Time Approach to Non-Relativistic Quantum Mechanics

Related

• Canonical Transformations in Quantum Mechanics
• Canonical equations of Hamilton for the nonlinear Schrödinger equation
• Mapping of solutions of the Hamilton-Jacobi equation by an arbitrary canonical transformation
• Canonical equations of Hamilton with beautiful symmetry
• Effects of transformed Hamiltonians on Hamilton-Jacobi theory in view of a stronger connection to wave mechanics