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Dirac equation in presence of the Hartmann and Higgs oscillator superintegrable potentials with the spin and pseudospin symmetries
Preview AbstractThe spin and pseudospin symmetries in the Dirac Hamiltonian are investigated in the presence of the Hartmann and the Higgs oscillator superintegrable potentials. The Pauli-Dirac representation is used in the Dirac equation with scalar and vector potentials of equal magnitude. Then, the Dirac equation is reduced to a Schrödinger-like equation. The symmetry algebras of the Schrödinger-like equation corresponding to the superintegrable potentials are represented. Also, the associated irreducible representations are shown by means of the quadratic algebras. Finally, the relativistic energy spectra of the Hartmann and the Higgs oscillator superintegrable potentials are calculated.