Random matrices and quantum Hamilton-Jacobi method
Department of Physics, BITS Pilani, Hyderabad Campus, Jawahar Nagar, Kapra Mandal, Medchal Dist, 500 078, Hyderabad, Telangana, India
Accepted: 27 November 2021
Published online: 16 December 2021
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.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021