Why are the mathematical descriptions of atomic processes in CQM better than their quantum mechanical counterparts?

Quantum mechanical calculations, generally, are statistical approximations of the actual closed-form solutions to the wave equations of CQM. This applies to more modern theories like QED and QCD, too. This is an area where much validation is still needed, because while quantum mechanics is well-tested experimentally, CQM must be able to explain the same data.

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