What is the physical process? How can Electron absorb Photon and then spontaneously release it after jumping orbits and then back to the original orbit?
This question has been entirely solved by Erwin Schrödinger in 1926: Article An Undulatory Theory of the Mechanics of Atoms and Molecules
Alas with two absentmindedness, but easy to address : he forgot to come back under the relativistic frame, so the two beating frequency are as wrong as possible (only the relativistic frame gives the correct ones), and he forgot to mention that the absorption of a photon gives the same beating between an initial state and a final state. Though it had already been proved by Gustav Kirchhoff in 1859.
The next step further is the transactional microphysics, which explores the laws of the transactions emerging from the Broglian ground noise.