# Why not describing the radiation of atom spectrum by TDSE instead of TISE?

The radiation of an atom was interpreted by time-independent schrodinger equation:electron was transformed from high energy level state to lower and emit a photon.

Could we treat this process through a wavefunction ${\psi}(t)$? Before emiting,the system's wavefunction is ${\psi}(0)$ and after emiting photon,it is ${\psi}(t_0)$. ${\psi}(t)$ is constrained by time-dependent schrodinger equation and contain all information of the system.

Is there any papers incorporate photon emiting in wavefunction as well as the method to define ${\psi}(t=0)$?