Quantum Potential Via General Hamilton - Jacobi Equation

TL;DR

This paper explores how quantum potential naturally arises in the general Hamilton-Jacobi framework through quantum canonical transformations, without relying on wave functions, and extends the approach to relativistic cases.

Contribution

It demonstrates the emergence of quantum potential in Hamilton-Jacobi theory without wave functions and extends the method to relativistic regimes.

Findings

Quantum potential appears via commuting relations and transformations.

The approach is valid in both non-relativistic and relativistic regimes.

Quantum kinetic energy is incorporated into the framework.

Abstract

In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The interpretation of QP in terms of independent entity is discussed along with the introduction of quantum kinetic energy. The method has been extended to relativistic regime, and same results have been concluded.