Exact solution of the dirac equation for an inhomogeneous magnetic field

The two-component Dirac equation for the case of an electron in the inhomogeneous magnetic field Hx(y) = H/(I -ay)2 is solved exactly. Explicit expressions for the bound-state energy eigenvalues and eigenfunctions are given. Further, the exact solutions for certain related field configurations are also indicated. © 1983 Società Italiana di Fisica.