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Exact solutions of the Dirac equation with harmonic oscillator potential including a Coulomb-like tensor potential. (English) Zbl 1168.81324

Summary: We study the Dirac equation with scalar, vector, and tensor interactions. The Dirac Hamiltonian contains quadratic scalar and vector potentials, as well as a tensor potential. The tensor potential is taken as a sum of a linear term and a Coulomb-like term. It is shown that the tensor potential preserves the form of the harmonic oscillator potential and generates spin-orbit terms. The energy eigenvalues and the corresponding eigenfunctions are obtained for different alternatives.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
34C40 Ordinary differential equations and systems on manifolds
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