Since I’m in a good mood today and the majority of my peers skipped one of the most interesting courses.
How to learn quantum physics (the fundamentals of it, anyway)
1) Prerequisites. Integration, derivatives and partial derivatives should have been practiced ad nauseum at this point. A good grasp on linear algebra and basics of operators will also come in handy, as well as some complex analysis.
2) Classical mechanics. Yes, you have to know it, at least remember the basics, because it makes your life easier. Ideally, learn some Lagrange mechanics, since it teaches you to think in terms of energy rather than path. You’ll also need Coulomb’s law and centripetal acceleration for deriving Bohr’s atom model.
3) The first few chapters should be taught hand-to-hand with experiment and history. If your curiculum doesn’t provide this for some reason - go to youtube or even look experiments up on wikipedia. Learning concepts is easier when they are tied to real world at least in some way. At least know that Planck’s formula basically describes an oven.
4) The more advanced stuff will feel challenging. In the first part of the curriculum the sequence is always the same: make some assumptions about the system’s structure (e.g. electron in a potential well), from them obtain a hamiltonian, use Schrodinger’s equation to build a differential equation, then solve it using some gimmicks from differential equations course. The solution’s form is usually given in advance or supposed from the equation’s type.
5) Quantum mechanics is all about approximations: the only equations you will sovle precisely are for hydrogen atom and for an electron in some electrical or magnetic field. Everything else will imply some sort of approximation; learn them first, the rest can be derived.
