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Electric to be

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For a hydrogen atom, the wave function of the electron is found by using the hydrogen proton as an external potential and proceeding from there to find discrete energy levels eigenvalues.

Then, this electron can be excited by accepting photons of discrete energies. Sure, makes sense. Now although I may be speaking nonsense, I know that all electric and magnetic fields have an energy density that is proportional to the field strength squared. I also know that a photon is roughly modeled as the particle manifestation of an electromagnetic wave, which is basically a changing electric and magnetic field, propagated according to Maxwell'a equation.

Why is it that the energy from this electric and magnetic field, which is propagating can be accepted by the electron, but the energy stored in the static electric field of the potential field which is used to solve the schrodinger equation, cannot be?

Thank you.