Approximation Methods for Stationary States
In several of the preceding chapters we have discussed application of the postulates of quantum mechanics to several important types of examples. Although these applications were varied, there is one common characteristic shared by all of them. In each case, the Schrödinger equation could be solved exactly for the eigenvalues and associated eigenfunctions. If this were possible for all problems of interest to chemists, our insight into the nature of chemical phenomena would certainly be increased enormously. However, the fact is that only a very few problems are solvable exactly. In particular, it has not yet been possible to obtain an exact solution to the Schrödinger equation for any system containing more than one electron. Consequently, our knowledge of chemistry as revealed through quantum mechanics has been restricted primarily to that obtainable from an examination of approximate solutions to the Schrödinger equation. However, the advent of large-scale computers has greatly expanded both the accuracy and the scope of approximate solutions that can be obtained. We shall now discuss some of the methods that are available for obtaining approximate solutions to the Schrödinger equation for stationary states, and that form the basis for most applications of quantum mechanics to chemical problems.
KeywordsPerturbation Theory External Electric Field Helium Atom Trial Function Unperturbed System
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