Saddle-point variational method for relativistic excited states

The saddle-point variational (SPV) method is applied to the n=2 excited states of the Dirac equation for a Coulomb potential. The variational energies agree well with the exact energy for quite large coupling strength (\ensuremath{\lambda}=0.4 and 0.8). Fine-structure differences are also well reproduced. An extended SPV method gives better results than explicit orthogonalization of the variational states.