Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics

Journal Article · Thu Jan 15 04:00:00 EST 2009 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2008.07.003· OSTI ID:21167702

Ci, Song ^[1]

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1. Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China)

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.

• OSTI ID: 21167702
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 324; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CASIMIR OPERATORS
DIRAC EQUATION
ENERGY SPECTRA
HAMILTONIANS
HARMONIC OSCILLATORS
HYDROGEN
ORBITAL ANGULAR MOMENTUM
POTENTIALS
QUANTUM MECHANICS
RELATIVISTIC RANGE
SO-3 GROUPS
SU-2 GROUPS
SYMMETRY
TWO-DIMENSIONAL CALCULATIONS