The Schrödinger Equation for the Hydrogen Atom: A generalization

This is a two-body problem (diatomic molecule) and formulation of the problem is possible:

https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_110A%3A_Physical_Chemistry_I/Text/06%3A_The_Hydrogen_Atom/6.01%3A_The_Schrodinger_Equation_for_the_Hydrogen_Atom_Can_Be_Solved_Exactly

And its solution is using Spherical Harmonics:

http://mathworld.wolfram.com/SphericalHarmonic.html

So how about 3-body, or n-body system?

How complexity creeps in arising from n-bodies to n-1 bodies interaction?

https://gereshes.com/2018/05/07/what-is-the-n-body-problem/   

https://www.youtube.com/watch?v=09iTidqkriw  (very good video on the history)

and the github for the codes mentioned above is here:

https://github.com/winsmith/n-body-problem

Complex, but simulation is possible:

https://jheer.github.io/barnes-hut/  (this is interactive)

https://en.wikipedia.org/wiki/N-body_simulation

https://arxiv.org/abs/astro-ph/0503600 

 https://www.americanscientist.org/article/the-100-billion-body-problem

https://sites.math.washington.edu/~morrow/336_13/papers/peter.pdf 

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.762.6900&rep=rep1&type=pdf 

http://users.wfu.edu/choss/CUDA/docs/Lecture%2012.pdf 

http://www.math.harvard.edu/archive/118r_spring_05/handouts/nbody.pdf 

https://www.cs.cmu.edu/~guyb/realworld/nbody.html 

https://www.math.arizona.edu/~dwang/485home-10/N-body.pdf