Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics

Details Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics

2008-04-25

arxiv.org/abs/0804.4063v3

Physics

Quantum Physics

3 pages, Accepted by Annals of Physics (New York)

Scientific paper

10.1016/j.aop.2008.07.003

The two-dimensional Dirac Hamiltonian with equal scalar and vector potentials has been proved commuting with the deformed orbital angular momentum $L$. When the potential takes the Coulomb form, the system has an SO(3) symmetry, and similarly the harmonic oscillator potential possesses an SU(2) symmetry. The generators of the symmetric groups are derived for these two systems separately. The corresponding energy spectra are yielded naturally from the Casimir operators. Their non-relativistic limits are also discussed.

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