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arXiv · 0809.1929

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

A. Poszwa·A. Rutkowski
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Abstract

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 $μ$ of the operator $j_{z}$, two quantum numbers $η$ and $κ$ are introduced as eigenvalues of hermitian operators $P=βσ_{z}'$ and $K=β(σ_{z}'l_{z}+1/2)$, 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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A. Poszwa, A. Rutkowski. 2008-09-11. Two-dimensional relativistic hydrogenic atoms: A complete set of constants of motion. https://arxiv.org/abs/0809.1929

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