/sci/ - Science & Math

Math major here, I'd like to see a mathematical derivation of the shapes of atomic orbitals that we see in s orbitals, p orbitals and so on, as well as derivation of hybrid orbitals. All I know about quantum physics is that electrons are not particles but instead of probability distributions that get instantiated when observed. I'd like to start with the fundamentals of quantum theory from a mathematical perspective all the way up to atomic orbitals. How should I start?

The music and scenery with the train rolling through the greenery is nice, I guess flat earthers really are correct huh

Here we post and solve maths problems of the undergraduate competition/olympiad style. Make sure the problems are of a decent difficulty (not too easy or hard). Homework should go to /sqt/, it will be obvious which problems are homework.

I'll start:

[math]\text{Let} \ \{x_k \} \ \text{be a sequence of distinct positive integers. show that for all such sequences: } \ \sum_{k=1}^n \frac{1}{k} < \sum_{k=1}^n \frac{x_k}{k^2} \ \text{, for all natural numbers} \ n [/math]

What do you think /sci? Has anyone contributed more to rocketry than this man?