There are various calculational methods beyond the perturbation theory of thethat can be applied in specific circumstances to give either exact or approximate results. In this chapter some of the most common methods are explained. We start with the Rayleigh–Ritz variational method that can be used to obtain an upper-bound estimate of the ground-state energy of a quantum-mechanical system. Next we examine multi-electron atoms. In such a case simple application of perturbation theory becomes difficult and more needs to be done.
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