When solving the hydrogen atom in non relativistic quantum mechanics we use Coulomb's potential, $\sim1/r$, to describe the interaction between the proton and the electron.
I am worried about two conceptual points:
1-Wouldn't this potential be modified as r becomes smaller and smaller? (because now the electron will feel different potential at very short distances because then it can see 3 quarks with different charges, not a point like proton)
2-Also very short distances means very strong electric field, strong enough for particle anti particle creation, hence we do not have non relativistic quantum mechanics anymore, specially when the number of particles is not conserved.
Then what justifies our solution of the hydrogen atom without taking the previous two points into account?