On the exact description of the Dirac particle in the scalar and pseudoscalar fields

The problem of the exact solutions of the Dirac equation in the presence of the scalar and pseudoscalar fields is investigated by means of an algebraic method. Such an approach allows the author to find all the configurations of the scalar and pseudoscalar fields where separation of variables is possible. Some general recommendations for the search of exact solutions of the Dirac equation in Cartesian coordinates are proposed and some exact solutions in curvilinear coordinates are discussed.