The introduction of the quantum kinetic energy term via the Hamilton-Jacobi approach

摘要

In this work, the quantum Hamilton-Jacobi equation, according to the Roncadelli and Schulman method, with some relevant modifications, and based on the de Broglie-Bohm approach to quantum mechanics, has been rewritten; also it has been extended to the relativistic regime. Then, based on the results, we have introduced a term as "quantum kinetic energy" which could provide a meaningful link between the Brownian theory and the nature of the wave function, once the existence of an additional real space-filling fluid has been accepted.