Relativistic Motion in a Magnetic Field

A simple integral of the relativistic equations of motion for a charge in a magnetic field is used to reduce the Dirac equations to two simultaneous first-order differential equations. Eigenstates of this integral are the basis for a treatment of degeneracy and, in the case of a homogeneous field, for the construction of energy eigenfunctions from non-relativistic solutions. For a free particle the same integral leads directly to the only possible energy states with exactly defined spin projections.