Dirac Operator with Coulomb Field

  • D. M. Gitman
  • I. V. Tyutin
  • B. L. Voronov
Part of the Progress in Mathematical Physics book series (PMP, volume 62)


We consider a Dirac particle moving in the Coulomb field of a point charge Ze. We define the self-adjoint Dirac Hamiltonian with the Coulomb field for any real Z and solve the corresponding spectral problem. From a mathematical standpoint, the definition of the Dirac Hamiltonian as a self-adjoint operator for arbitrary Z presents no problem; in particular, the well-known “Z = 137 catastrophe” does not arise. A specific feature of the overcritical charges (Z > 137) is a nonuniqueness of the self-adjoint Dirac Hamiltonian, but this nonuniqueness is characteristic even for charges Z ≥ 119.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • D. M. Gitman
    • 1
  • I. V. Tyutin
    • 2
  • B. L. Voronov
    • 2
  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrasil
  2. 2.Department of Theoretical PhysicsP.N. Lebedev Physical InstituteMoscowRussia

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