## A $4\times 4$ Diagonal Matrix Schr{\"o}dinger Equation from Relativistic Total Energy with a $2\times 2$ Lorentz Invariant Solution.

**Authors:** Han Geurdes

In this paper an algebraic method is presented to derive a non-Hermitian Schr{\"o}dinger equation from $E=V+c\sqrt{m^2c^2+\left(\mathbf{p}-\frac{e}{c}\mathbf{A}\right)^2}$ with $E\rightarrow i\hbar \frac{\partial}{\partial t}$ and $\mathbf{p} \rightarrow -i\hbar \nabla$.
In the derivation no use is made of Dirac's method of four vectors and the root operator isn't squared either.
In this paper use is made of the algebra of operators to derive a matrix Schr{\"o}dinger equation. It is demonstrated that the obtained equation is Lorentz invariant.

**Comments:** 5 Pages.

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### Submission history

[v1] 2017-09-21 03:02:58

[v2] 2017-10-13 04:56:42

**Unique-IP document downloads:** 43 times

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