Two special variational techniques, the Lehmann-Maehly (LM) method and
the Kato method, recently proposed for solving the one-electron Dirac
equation without variational collapse are investigated hen in detail.
Both methods represent significant progress compared to the tradition
al variational techniques because each of them provides rigorous upper
and lower bounds to relativistic binding energies. A careful theoreti
cal examination, however, reveals that only the LM method can be regar
ded as a radical solution of all the problems related to variational c
ollapse. A numerical application to the Dirac equation for the hydroge
n atom in a uniform magnetic field confirms this conclusion and shows
as well that the LM method is also capable of yielding extremely accur
ate results and that the Kato method, in spite of a few limitations, r
epresents in any case a useful approach.