Physics – Quantum Physics
Scientific paper
2008-09-11
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.
Poszwa Anne
Rutkowski Artur
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