Relativistic Quantum Mechanics


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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 ), and the Klein-Gordon equation for particles of spin 0.

I. IU. KOBZAREV

References in periodicals archive ?
To establish the relativistic covariance of obtained quantum mechanics, we first developed manifestly relativistic quantum mechanics of two-component Klein-Gordon equation.
Mironov, "Octonic second-order equations of relativistic quantum mechanics," Journal of Mathematical Physics, vol.
Mironov, "Sedeonic generalization of relativistic quantum mechanics," International Journal of Modern Physics A, vol.
In this paper, we investigate the problem of whether Lorentz invariance is violated in noncommutative relativistic quantum mechanics regime.
Although the standard relativistic quantum mechanics does not take into account any minimal length scale, it is believed that, due to the correspondence principle in the continuum limit, the flat limit of quantum gravity will be reduced to this standard theory.
We find a candidate of stable algebra for relativistic quantum mechanics [29],
Strange, Relativistic Quantum Mechanics, Oxford University Press, Oxford, NY, USA, 1998.
As first relativistic scattering problem in q-deformed version of relativistic quantum mechanics, scattering from a Dirac delta potential is done in Section 4.
In recent years, the Dirac equation with different potentials in relativistic quantum mechanics with spin and pseudospin symmetry has been investigated [16-25].

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