Relativistic Quantum Mechanics

the branch of theoretical physics that studies the relativistic (that is, satisfying the requirements of the theory of relativity) quantum laws of motion of microparticles, such as electrons, in what is known as the single-particle approximation.

Relativistic effects are great when the energy of a particle is comparable with its rest energy. At such energies, the production of real or virtual particles may occur. For this reason, the single-particle approximation cannot be used in the general case. A consistent description of the properties of relativistic quantum particles is possible only within the framework of quantum field theory. In some problems where relativistic effects are significant, however, particle production need not be taken into consideration, and wave equations describing the motion of one particle—the single-particle approximation—can be used. The relativistic corrections to atomic energy levels (fine structure), for example, are found in this way. This approach based on the single-particle approximation is logically unclosed. Thus, in contrast to relativistic quantum field theory and nonrelativistic quantum mechanics, relativistic quantum mechanics, in which problems of this type are considered, does not constitute a consistent theory.

Relativistic generalizations of the Schrödinger equation are the basis for calculations in relativistic quantum mechanics: the Dirac equation for electrons and other particles of spin ½ (in units of Planck’s constant ℏ), and the Klein-Gordon equation for particles of spin 0.