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Quote by James Jackson
 Quote by Juan R. There is not relativistic quantum mechanics. In fact, it cannot exist.
Errm, what? As a (simple) example, the Dirac equation is the result of making Schrodinger's Equation Lorentz invarient.
No. It is not so simple. Dirac equation is incosistent and the developing of relativistic quantum mechanics is imposible. This is the reason of that Dirac equation was abandoned in relativistic quantum field theory, where the basic dinamical equation is a Schrodinger like one.

$$i \hbar \frac{\partial \Psi}{ \partial t} = H \Psi$$

Note: Dirac equation is not the result of making Schrodinger's Equation Lorentz invarient: that is the well-known relativistic Schrodinger equation.

Dirac equation was derived from the searching of a first order (in time) representation of Klein-Gordon equation more spin corrections for hidrogen atom.