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##### Pseudospin and spin symmetries in the relativistic harmonic oscillator

**Authors**: P. Alberto, A. Castro, M. Malheiro, R. Lisboa

**Ref.**: Bled Workshops in Physics, ISSN 1580-4992 - Proceedings of the Mini-Workshop Progress in Quark Models **7**, 1-6 (2006)

**Abstract**: We compute the analytical solutions of the generalized relativistic harmonic oscillator in 1+1 dimensions, including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. These are the conditions in which pseudospin or spin symmetries can be realized. We consider positive and negative quadratic potentials and present their bound-state solutions for fermions and antifermions. We relate the spin-type and pseudospin-type spectra through charge conjugation and gamma^5 chiral transformations. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.