The relativistic quantum hydrodynamic representation of Klein-Gordon equation
Quantum Physics
2015-09-22 v2
Abstract
The quantum hydrodynamic-like equations for two real variables (i.e., the phase and the amplitude of the wave function) of the relativistic Klein-Gordon equation are derived in the present paper. The paper also shows that in classical limit the hydrodynamic Klein-Gordon equations lead to the Madelung pseudo-potential [1] as well as to the quantum pseudo potential for a charged particle given by Janossy [2] and by Bialynicki et al [3]. The origin of the non-local interactions of quantum mechanics in the hydrodynamic model are discussed both for free and charged particles.
Keywords
Cite
@article{arxiv.1403.4598,
title = {The relativistic quantum hydrodynamic representation of Klein-Gordon equation},
author = {Piero Chiarelli},
journal= {arXiv preprint arXiv:1403.4598},
year = {2015}
}