How does an electron lose energy during quantum leaps?

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The electron is in an electric field which is conservative, it conserves mechanical energy. So how does it release a photon of energy hf as it moves from a higher energy level to a lower energy level?
 

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The motion of a classical charged point mass in an electric field is consevative, but a bound electron is not a classical point mass. It has a total energy, but there's no meaningful way of dividing that energy between potential energy and mechanical energy so the notion of conservative forces doesn't make any sense for a bound electron.

To really see how this works, you need a quantum mechanical instead of a classical model of the electron.
 
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