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

Maedeh Mollai; Mohammad Razavi; Safa Jami; Ali Ahanj

doi:10.1140/epjp/i2013-13001-9

EPJ

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

Maedeh Mollai¹, Mohammad Razavi¹, Safa Jami¹ and Ali Ahanj²^,3

¹ Department of Physics, Islamic Azad University, Mashhad Branch, Mashhad, Iran
² Department of Physics, Khayyam Higher Education Institute (KHEI), Mashhad, Iran
³ School of Physics, Institute for Research in Fundamental Science (IPM), Tehran, Iran

Received: 8 May 2012
Revised: 4 December 2012
Accepted: 6 December 2012
Published online: 7 January 2013

Abstract

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.