Two-dimensional relativistic hydrogenic atoms: A complete set of constants of motion
Abstract
Description
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.
6 pages
6 pages