Two-dimensional relativistic hydrogenic atoms: A complete set of constants of motion

Details Two-dimensional relativistic hydrogenic atoms: A complete set of constants of motion Two-dimensional relativistic hydrogenic atoms: A complete set of constants of motion

2008-09-11

arxiv.org/abs/0809.1929v1

Physics

Quantum Physics

6 pages

Scientific paper

The complete set of operators commuting with the Dirac Hamiltonian and exact analytic solution of the Dirac equation for the two-dimensional Coulomb potential is presented. Beyond the eigenvalue $\mu$ of the operator $j_{z}$, two quantum numbers $\eta$ and $\kappa$ are introduced as eigenvalues of hermitian operators $P=\beta\sigma_{z}'$ and $K=\beta(\sigma_{z}'l_{z}+1/2)$, respectively. The classification of states according to the full set of constants of motion without referring to the non-relativistic limit is proposed. The linear Paschen-Back effect is analyzed using exact field-free wave-functions as a zero-order approximation.

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