Two electrons, or an electron and a proton, interact with each other because of the Coulomb potential, which can also be seen in the Schrödinger equation (which is the equation that describes the motion for elementary particles).
But how do an electron and a photon interact? Why can a photon kick up an electron to a higher atomic orbital, or why is a photon emitted when an electron jumps down to a lower orbital? A photon do not have any charge, so the interaction cannot be caused by the Coulomb potential. So what is it that causes the interaction, and how does that affect the Schrödinger equation? (Or well, the relativistic version of the Schrödinger equation, since we're dealing with photons.)
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