Sources such as Eugene Hecht and Griffiths claim that oscillating electric dipole radiation is a great approximation for radiation generated from atoms and molecules during electronic transitions. I don't really understand why this is true.
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$\begingroup$ What alternatives do you have in mind? $\endgroup$– RuslanCommented Apr 6, 2021 at 9:09
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1$\begingroup$ It isn't an exact duplicate, but see the question Is there oscillating charge in a hydrogen atom?. Emilio Pisanty's answer gives a wonderful description of how an oscillating dipole exists in an atom that is in a superposition of eigenstates. It's this dipole that creates the radiation. $\endgroup$– John RennieCommented Apr 6, 2021 at 9:22
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It seems that they refer to the dipole approximation, which is not the same as describing the radiation as that of an oscillating dipole (the description that work well for antennas, but not for atoms). The essence of the approximation is that the interaction between the atom and the electric field can be represented as $$ H=-\mathbf{d}\cdot\mathbf{E}, $$ where $\mathbf{d}$ is the dipole moment and $\mathbf{E}$ is the eletric field. The approximation is made possible by the smallness of the atoms (about $0.1$nm in size) in comparison to the typical electromagnetic field wave lengths (e.g., a few hundred nanometers in visible range). Here is my post that gives a bit more mathematical details.
In some cases, notably when the dipole moment is zero, one has to resort to higher-order approximations (quadrupole, octupole, etc.)
