Hypervirial and Hellmann-Feynman theorems applied to the calculation of energy levels for relativistic particles

The nonrelativistic hypervirial Hellmann-Feynman method developed recently is extended to deal with relativistic particles bound in a spherically symmetric potential. A simple analytical procedure for calculating correction terms of arbitrary high orders is derived. Numerical results obtained through a study of the screened Coulomb potential enable us to illustrate the improvements of our procedure over the previous approaches.