The relativistic virial theorem by the elimination method and nonrelativistic approximations to this theorem

The relativistic virial theorem for bound states of a particle is derived within the framework of the elimination method by the use of Fock's variational argument. The variational equation and the virial theorem involving only the large component of the Dirac wavefunction are deduced in closed form. The general formulae are illustrated for the case of the relativistic electron in an electrostatic central field. By use of series expansions, a nonrelativistic approximation to the virial theorem up to second order in the fine-structure constant is obtained.