Ken,
I fear this may be a rather trickier task then you think.
The first problem is that stellar atmospheres are not in thermal equilibrium. There’s convection going on, dredging up hot gas to the surface, which then cools and sinks back down. The cooling gas is not in thermal equilibrium.
Furthermore, stellar atmospheres are translucent: light can penetrate a certain depth into the atmosphere. Temperature and pressure change with depth. This means that to model a stellar spectrum you need to do ray-tracing through a finite depth of partially opaque medium, modelling absorption, emission, and photon scattering. This is the branch of astrophysics called radiative transfer.
And to make things worse, the quantum mechanical equations for atomic line spectra are not soluble for anything more complicated than hydrogen. Computational models of bigger atoms exist, but they’re notoriously inaccurate. To be sure of what an atom’s spectrum looks like, you really need to measure it empirically in a laboratory. But that’s hard, because it involves recreating the conditions at the surface of the Sun. Atoms need to be exceedingly hot to reach the ionisation states they attain in the Sun. So you need a very large laser, some very hot and very pure samples of each chemical element, and a very fast camera that can measure the spectrum of the plasma formed after the laser fires.
To compound the challenge, there are > 100 elements in the periodic table, each of which can have N-1 ionisation states, leading to thousands of atomic states, each with distinct spectra. And that’s just the atoms – stellar atmospheres have molecules too.
I have professional experience working with a couple of codes which attempt to model all of the above, and each is the culmination of several PhDs worth of work. Turbospectrum (Bertrand Plez et al. 2012) is simpler and open source. PySME (Nikolai Piskunov et al. 2018) is more sophisticated in its modelling of non-equilibrium effects, and is available in binary form online but not open source. Both rely on the VALD list of atomic lines – maintained at Uppsala University – which is essentially a synopsis of a vast number of laboratory studies. The oscillator strengths in there are mostly not calculated by quantum mechanics; they’re fitted to empirical data. Quantum mechanics may allow you to write down equations for oscillator strengths, but that’s not much good if they can’t be solved.
I hope that’s vaguely helpful.
Best wishes,
Dominic