Abstract
A relativistic version of the variational perturbation method is extended to apply to excited states of the Dirac equation. It is proved that the value of the Hylleraas functional is an upper bound to the exact second-order (proportional to c−4) correction to the energy. In order to demonstrate the usefulness of this approach to the problem of optimising non-linear parameters the method is applied to the special case of hydrogen-like atoms. The first-order relativistic corrections to the wavefunctions for some s, p and d states have been approximated in terms of expontential functions.
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