Random Matrices and Quantum Hamilton-Jacobi Method
arXiv:2107.06494 · doi:10.1140/epjs/s11734-021-00363-y
Abstract
In this paper, we start with the quantum Hamilton-Jacobi approach and show that the underlying complex pole evolution of the Schrödinger 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.
some of the content has overlap with arXiv:1801.00544 [quant-ph] and arXiv:1501.06665 [quant-ph]