Atomic (electron) recombination via the Schrodinger Equation Photon radiative transitions are often modeled from electron bound state (e.g. in an atomic potential) to the continuum (free states).  However, I've never seen the inverse process (recombination) described via the Schrodinger Equation.  My question therefore is:
Can you model electron recombination with the Schrodinger Equation?  If (as I assume) not, then what is the most straightforward way to examine transitions from the continuum back to bound states?
 A: You are asking in essence whether the emission of a photon due to the transition of an electron from a free, unbound high energy state to a bound low energy state of the atom can be modeled by using only the Schroedinger equation. While it is known that time-dependent perturbation theory can be used to find solution of the Schroedinger equation to calculate the transition rate of an electron from a low energy quantum state to a high energy bound or free state due to photon absorption, and also for stimulated emission of a photon with an electron transitioning from a high bound state to a low bound state in an atom, it cannot be done using Schroedinger's equation alone in the case of spontaneous emission of a photon when an electron makes a transition from a high (bound or unbound) state. The reason is that you need a wave function for the whole system including the quantized electromagnetic field. The latter can be represented by quantized harmonic oscillators. With this you can again use time-dependent perturbation theory and Fermi's Golden Rule to arrive at a transition rate from a high energy bound state to a low energy bound state in the atom. I have found this link to a Cambridge University lecture where you find the derivation [Radiative Transitions].1 I think that for the capture of a free electron on an atom and emission of a photon there should exist a similar model using Schroedinger's equation and the simple quantum harmonic oscillator model for the quantized electromagnetic field. 
