General solution of the Dirac equation with the Coulomb potential
- URL: http://arxiv.org/abs/2009.09838v1
- Date: Thu, 17 Sep 2020 10:39:03 GMT
- Title: General solution of the Dirac equation with the Coulomb potential
- Authors: A. A. Eremko, L. Brizhik, and V. M. Loktev
- Abstract summary: The general solution of the Dirac equation with the Coulomb potential is shown to contain free parameters.
The spatial distributions of these characteristics are shown to depend essentially on the invariant set.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The Dirac equation with the Coulomb potential is studied. It is shown that
there exists a new invariant in addition to the known Dirac and Johnson-Lippman
ones. The solution of the Dirac equation, using the generalized invariant, and
explicit expressions for the bispinors corresponding to the three sets of the
invariants, their eigenvalues and quantum numbers are obtained. The general
solution of the Dirac equation with the Coulomb potential is shown to contain
free parameters, whose variation transforms one particular solution into any
other and controls spatial electron probability amplitude and spin
polarization. The electron probability densities and spin polarizations are
obtained in the general form and calculated explicitly for some electron states
in the hydrogen-like energy spectrum. The spatial distributions of these
characteristics are shown to depend essentially on the invariant set,
demonstrating physical difference of the states corresponding to different
invariants.
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