Galilean covariant Dirac equation with a Woods–Saxon potential

We derive and solve the Galilean covariant Dirac equation, also called 'Levy-Leblond equation', for spin-½ particles in a Woods–Saxon potential. We obtain this wave equation with a Galilean covariant approach, which is based on a (4+1)-dimensional manifold with light-cone coordinates followed by a reduction to the (3+1)-dimensional Galilean space-time. We apply the Pekeris approximation and exploit the Nikiforov–Uvarov method to find the energy eigenvalues and eigenfunctions. (author)