Phys. Rev. Lett. 95, 252501 (2005) [3 pages]U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic OscillatorReceived 12 August 2005; published 13 December 2005 We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but a U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.95.252501
DOI:
10.1103/PhysRevLett.95.252501
PACS:
21.60.−n, 02.20.−a, 21.10.−k
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