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We have seen, in Sect. 9.4, that we can solve Schrödinger's equation exactly to find the stationary eigenstates of a hydrogen atom. Unfortunately, it is not possible to find exact solutions of Schrödinger's equation for atoms more complicated than hydrogen, or for molecules. In such systems, the best that we can do is to find approximate solutions. Most of the methods which have been developed for finding such solutions employ the so-called variational principle discussed below.

Richard Fitzpatrick 2010-07-20