Typically (in popular literature) the process of photon emission by an excited atom is considered as an instant event. But actually it is quite likely that it is a continuous process. Such processes are usually described by evolutionary differential equations (ODEs or PDEs). Assume that we consider a hydrohen atom composed by 1 proton(adsbygoogle = window.adsbygoogle || []).push({}); pand 1 electrone. Let [itex]\Psi(t,x_p,y_p,z_p,x_e,y_e,z_e )[/itex] be the time dependent wave function of the atom. The time dependent Shrödinger equation with the Coulomb potential can be written for this function. How many auxiliary functions should be added for describing the photon which is absent in the beginning of the process and which is present in the end of it? How many auxilioary terms should be added to the time-dependent Shrödinger equation? It would be best to see the complete system of differential equations.

The creation/annihilation operators could be used in deriving these differential equtions, but they should not enter the ultimate equations. These should be differential equations for functions, not for operators.

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# Photon emission by an excited hydrogen atom

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