The angular momentum operator in the Dirac equation

Abstract

The Dirac equation in spherically symmetric fields is separated in two different tetrad frames. One is the standard Cartesian (fixed) frame and the other is the diagonal (rotating) frame. After separating variables in the Dirac equation in spherical coordinates, and solving the corresponding eigenvalue equations associated with the angular operators, we obtain that the spinor solution in the rotating frame can be expressed in terms of Jacobi polynomials, and it is related to the standard spherical harmonics, which are the basis solution of the angular momentum in the Cartesian tetrad, by a similarity transformation.