Gv. Shishkin, ON THE EXACT DESCRIPTION OF THE DIRAC PARTICLE IN THE SCALAR AND PSEUDOSCALAR FIELDS, Journal of physics. A, mathematical and general, 26(16), 1993, pp. 4135-4146
The problem of the exact solutions of the Dirac equation in the presen
ce of the scalar and pseudoscalar fields is investigated by means of a
n algebraic method. Such an approach allows us to find all the configu
rations of the scalar and pseudoscalar fields where separation of vari
ables is possible. Some general recommendations for the search of exac
t solutions of the Dirac equation in Cartesian coordinates are propose
d and some exact solutions in curvilinear coordinates are discussed.