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Relativistic Harmonic Oscillator with Spin Symmetry

Joseph N. Ginocchio
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Abstract

The eigenfunctions and eigenenergies for a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials are derived. Equal scalar and vector potentials may be applicable to the spectrum of an antinucleion imbedded in a nucleus. Triaxial, axially deformed, and spherical oscillator potentials are considered. The spectrum has a spin symmetry for all cases and, for the spherical harmonic oscillator potential, a higher symmetry analogous to the SU(3) symmetry of the non-relativistic harmonic oscillator is discussed.

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Joseph N. Ginocchio. 2005-03-25. Relativistic Harmonic Oscillator with Spin Symmetry. https://doi.org/10.1103/physrevc.69.034318

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