Why does the orbital model consist of L-, K-, N-…shells if the location of the electrons cannot be predicted exactly?

I'm currently studying the orbital model, its origins, and its quantum mechanical background. What I still don't quite understand is this: If the model arises from the Schrödinger equation and its wave functions, why do shells even exist? Doesn't a shell contradict the quantum mechanical background of the model? Can't all electrons be anywhere? (Or…

Python and physics: Harmonic oscillator graphically up to n= 4?

I'd like to review the lectures I took at university. We were on the topic of harmonic oscillators, and I'd like to create a plot that looks something like this. However, up to n=4. So once the stationary (psi_n(x)) and once the probability of residence |psi_n(x)|^2 The parable is meant to represent the potential. The…