A 4 × 4 diagonal matrix Hermitian Schrödinger equation from relativistic total energy with a 2 × 2 Lorentz invariant relation between amplitude and phase

In this paper an algebraic method is presented to derive a 4 × 4 Hermitian Schrödinger equation from E=V+cm2c2+(p−ecA)2 with E→iℏ∂∂t and p→−iℏ∇. The latter operator replacement is a common procedure in a quantum description of the total energy. In the derivation we don't make use of Dirac's method of four vectors. Moreover, the root operator isn't squared either. Instead, use is made of the algebra of operators to derive a Hermitian matrix Schrödinger equation. We believe that new physics can be obtained from an alternative quantization of the relativistic total energy. Note e.g. the pion physics behind the Klein-Gordon equation and the antimatter behind the Dirac quantization of the total relativistic energy. In this paper, for the sake of clarity, a time-only dependence of the electromagnetic potential vector is assumed. It is also demonstrated that a “latent” Lorentz invariance exists related to a derived expression for amplitude and phase.