Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics. (English) Zbl 1159.81372
Summary: 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.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 70H40 | Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics |
| 81V45 | Atomic physics |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
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