Abstract
The universal quantum equation (UQE) is found to describe the transport properties of the quantum particles. This equation describes a wave equation interacting with constant scalar and vector potentials propagating in spacetime. A new transformation that sends the Schrodinger equation with a potential energy V = -1/2mc(2) to Dirac's equation is proposed. The Cattaneo telegraph equation as well as a one-dimensional UQE are compatible with our recently proposed generalized continuity equations. Furthermore, a new wave equation resulted from the invariance of the UQE under the post-Galilean transformations is derived. This equation is found to govern a Klein-Gordon's particle interacting with a photon-like vector field (ether) whose magnitude is proportional to the particle's mass.