Quantum multipole expansion questions

[Brent Van Neste]

If we would not introduce a multipole expansion, we would have to solve a system of a nucleus and electrons, which is not solvable for more than one electron if we do not use any approximations.
If we would try to do perturbation theory on such a system, we would not know which term could be regarded as a perturbation term. Due to the use of the multipole expansion, we know that the higher order multipole contributions in the expansion of the interaction terms are smaller and therefore can be used as the pertubation.

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