Dirac reduced radial equations and the problem of additional solutions

Anzor Khelashvili; Teimuraz Nadareishvili

doi:10.1142/s0218301317500434

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arXiv · 1610.07936

Dirac reduced radial equations and the problem of additional solutions

Anzor Khelashvili·Teimuraz Nadareishvili

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Abstract

We show that additional solutions must be ignored (in differences of the Schrodinger and Klein-Gordon equations) in the Dirac equation, where usually passed the second order radial equation, called the reduced equation, instead of a system. Analogously to the Schrodinger equation, in this process the Dirac delta function appears, which was unnoted during the full history of quantum mechanics. This unphysical term we remove by a boundary condition at the origin. However, the distribution theory imposes on the radial function strong restriction and by this reason practically for all potentials, even regular, use of these reduced equations is not permissible. At the end we include consideration in the framework of two-dimensional Dirac equation. We show that even here the additional solution does not survives as a result of usual physical requirements.

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Anzor Khelashvili, Teimuraz Nadareishvili. 2016-10-23. Dirac reduced radial equations and the problem of additional solutions. https://doi.org/10.1142/s0218301317500434

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