Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential. (English) Zbl 1227.81152

Summary: It is shown that the Dirac equation with scalar and vector quadratic potentials and a Coulomb-like tensor potential can be solved exactly. The bound state solutions for equal vector and scalar potentials are obtained. The limit of zero tensor coupling is investigated. The case of equal vector and scalar potentials with opposite sign is also studied. The pseudospin symmetry and its breaking by the tensor interaction are discussed.


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q80 Special quantum systems, such as solvable systems
81U15 Exactly and quasi-solvable systems arising in quantum theory
81V35 Nuclear physics
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