Solution of the Dirac equation with position-dependent mass in the Coulomb field. (English) Zbl 1118.81303
Summary: We obtain exact solution of the Dirac equation for a charged particle with position-dependent mass in the Coulomb field. The effective mass of the spinor has a relativistic component which is proportional to the square of the Compton wavelength and varies as \(1/r\). It is suggested that this model could be used as a tool in the renormalization of ultraviolet divergences in field theory. The discrete energy spectrum and spinor wave-function are obtained explicitly.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
Keywords:
Dirac equation; position-dependent mass; Coulomb potential; relativistic spectrum; renormalizationReferences:
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