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Chemistry LibreTexts

7: Approximation Methods

The Schrödinger equation for realistic systems quickly becomes unwieldy, and analytical solutions are only available for very simple systems - the ones we have described as fundamental systems in this module. Numerical approaches can cope with more complex problems, but are still (and will remain for a good while) limited by the available computer power. Approximations are necessary to cope with real systems. Within limits, we can use a pick and mix approach, i.e. use linear combinations of solutions of the fundamental systems to build up something akin to the real system. There are two mathematical techniques, perturbation and variation theory, which can provide a good approximation along with an estimate of its accuracy. These two approximation techniques are described in this chapter.