Regular perturbation theory of relativistic corrections: II. Algebraic approximation - art. no. 012508

A four-component equivalent of the Schrodinger equation, describing both th e nonrelativistic electron and the nonrelativistic positron, is introduced. The difference between this equation and the Dirac equation is treated as a perturbation. The relevant perturbation equations and formulas for correc tions to the energy are derived. Owing to the semibounded character of the Schrodinger Hamiltonian of the unperturbed equation the variational perturb ation method is formulated. The Hylleraas functionals become then either up per or lower bounds to the respective exact corrections to the energy. In o rder to demonstrate the usefulness of this approach to the problem of the v ariational optimization of nonlinear parameters, the perturbation correctio ns to wave functions for the of hydrogenlike atoms have been approximated i n terms of exponential basis functions. The Dime equation in this algebraic approximation is solved iteratively starting with the solution of the Schr odinger equation.