Random Matrices and Quantum Hamilton-Jacobi Method
Quantum Physics
2022-01-05 v1 Mathematical Physics
math.MP
Abstract
In this paper, we start with the quantum Hamilton-Jacobi approach and show that the underlying complex pole evolution of the Schr\"odinger equation is described by the quantum action in terms of a random matrix. The wave function is given by the random matrix probability distribution function. In literature this is known as the famous Cole-Hopf Transformation.
Cite
@article{arxiv.2107.06494,
title = {Random Matrices and Quantum Hamilton-Jacobi Method},
author = {K. Haritha and K. V. S. Shiv Chaitanya},
journal= {arXiv preprint arXiv:2107.06494},
year = {2022}
}
Comments
some of the content has overlap with arXiv:1801.00544 [quant-ph] and arXiv:1501.06665 [quant-ph]