Hamilton-Jacobi Approach to the Quantization of Classically Non-Separable but Integrable Two-Dimensional Systems: the Role of the Classical Caustics
Quantum Physics
2019-09-17 v1
Abstract
The quantization method based on the quantum Hamiltonian Jacobi equation, is extended to two-dimensional non-separable but integrable Hamiltonians. It is shown that each wave function for those systems corresponds to a well-defined family of classical trajectories, enveloped by a caustic. The energy eigenvalues and the values of the wave functions on the caustic are obtained by solving the 1-dim quantum Hamilton Jacobi equation of the caustic' arcs. Results are in good agreement with those obtained by usual methods.
Keywords
Cite
@article{arxiv.1909.06939,
title = {Hamilton-Jacobi Approach to the Quantization of Classically Non-Separable but Integrable Two-Dimensional Systems: the Role of the Classical Caustics},
author = {Mario Fusco Girard},
journal= {arXiv preprint arXiv:1909.06939},
year = {2019}
}
Comments
15 pages, 7 figures