Derivation of Dirac, Klein-Gordon, Schrodinger, Diffusion and quantum heat transport equations from a universal quantum wave equation

Abstract

A universal quantum wave equation that yields Dirac, Klein-Gordon, Schrodinger and quantum heat equations is derived. These equations are related by complex transformation of space, time and mass. The new symmetry exhibited by these equations is investigated. The universal quantum equation yields Dirac equation in two ways: firstly by replacing the particle my $m_0$ by $im_0$, and secondly by changing space and time coordinates by $it$ and $i\vec{r}$, respectively.