Comparison of the Variation and Perturbation Methods

The perturbation method applies to all the bound states of a system. Although the variation theorem stated in Section 8.1 applies only to the lowest state of a given symmetry, we can use the linear variation method to treat excited bound states. 

Perturbation calculations are often hard to do because of the need to evaluate the infinite sums over discrete states and integrals over continuum states that occur in the second-order and higher-order energy corrections. 

In the perturbation method, one can calculate the energy much more accurately (to order 2k + 1) than the wave function (to order k). The same situation holds in the variation method, where one can get a rather good energy with a rather inaccurate wave function if one calculates properties other than the energy, the results will generally not be as reliable as the calculated energy. 

Although most calculations of molecular wave functions have been done using the variation method, there has been a revival of interest in applying the perturbation method to such problems. See Section 15.18. 

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