Telegraph Equations and Complementary Dirac Equation from Brownian Movement

Balwant Singh Rajput

Physics Department, Kumaon University, Nainital, India.

DOI: 10.4236/jmp.2012.39128                

Abstract

Telegraph equations describing the particle densities in Brownian movement on a lattice site have been derived and it has been shown that the complementary classical Dirac equation appears naturally as the consequence of correlations in particle trajectories in Brownian movement. It has also been demonstrated that Heisenberg uncertainty relation between energy and time is the necessary and sufficient condition to transform this classical equation into usual Dirac’s relativistic quantum equation.

Keywords

Telegraph Equation; Dirac Equation; Brownian Motion; Analytic Continuation; Schrödinger Equation; Uncertainty Relations

Conflicts of Interest

The authors declare no conflicts of interest.

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