Relativistic Coulomb problem for Z larger than 137

Details Relativistic Coulomb problem for Z larger than 137 Relativistic Coulomb problem for Z larger than 137

2010-05-09

arxiv.org/abs/1005.1414v1

Int. J. Mod. Phys. A 25, 3703 (2010)

Physics

Quantum Physics

12 pages, 4 figures

Scientific paper

10.1142/S0217751X10049402

We propose a relativistic one-parameter Hermitian theory for the Coulomb problem with an electric charge greater than 137. In the non-relativistic limit, the theory becomes identical to the Schr\"odinger-Coulomb problem for all Z. Moreover, it agrees with the Dirac-Coulomb problem to order (\alph Z)^2, where \alpha is the fine structure constant. The vacuum in the theory is stable and does not suffer from the "charged vacuum" problem for all Z. Moreover, transition between positive and negative energy states could be eliminated. The relativistic bound states energy spectrum and corresponding spinor wavefunctions are obtained.

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