Abstract
In this chapter, we extend the study of the non-relativistic Schroedinger equation to the case of a particle having a speed approaching that of light, in a way that must be consistent with the Lorentz transformation equations of the special theory of relativity. A characteristic feature of relativistic wave equations is that spin arises naturally from the beginning and must not be added afterwards to the non-relativistic Schroedinger equation. After an introduction on Schroedinger’s attempt of reconsidering his wave equation in a relativistic way and on the related Klein–Gordon equation, we turn to Dirac’s relativistic quantum theory of the free electron, extending next our considerations to the relativistic theory of an electron in a central field, then to the one-electron atomic and molecular systems, followed by the two-electron atomic and molecular systems, and, finally, by a glance at the relativistic calculations on many-electron atoms and molecules.
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