Direct Diagonalization Versus Algebraic Approaches

Perturbation theory is an extremely useful analytic tool. It is almost always possible to treat a narrow range of. /-values in a multistate interaction problem by exactly diagonalizing a two-level problem after correcting, by nondegenerate perturbation theory or a Van Vleck transformation, for the effects of other nearby perturbers. Such a procedure can enable one to test for the sensitivity of the data set to the value of a specific unknown parameter. 

There is a good historical reason for the algebraic tradition in spectroscopy. Without computers, exact matrix diagonalizations were impossibly time consuming. There was no choice but to resort to algebraic formulas. Now there is a choice. 

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