Dirac equation of the electron in a magnetic field

To every solution of the time-independent Dirac equation for the electron in an arbitrary magnetic field there belongs a second solution. A characteristic twofold degeneracy, suggested by this circumstance, is shown to be excluded for the ground state at the energy $E=m{c}^2$,, with the further distinction of this state that the current density vanishes here at all points in space. The conditions under which the excited states exhibit such a degeneracy are discussed and in the case of its occurrence are shown to allow the construction of a particularly symmetrical pair of mutually orthogonal solutions.