Anyone know the best way to fully understand quantum theory (eg. Prerequisites)?

 

I already know some Classical Mechanics, and a bit of calculus, but I still have a hard time with QM. I know it conceptually, but knowing it mathematically is much more interesting.

You should have a good grasp of finite dimensional vector spaces and linear operators before reading up on topological vector spaces and in particular Hilbert spaces. A little analysis and how to solve differential equations would be useful.

 

Also, knowing a bit about the Hamiltonian formalism would be useful in seeing the parallels between classical and quantum as well as helping you with "quantisation".

I already know how to solve differential equations and I do have some Hamiltonian Formalism under my belt; I didn't understand anything you wrote about in the first paragraph. I guess I better read up then!

Didn't someone say: if you think you understand quantum mechanics, you don't understand quantum mechanics!

Didn't someone say: if you think you understand quantum mechanics, you don't understand quantum mechanics!

Yes, it is attributed to Feynman, but I am not sure if there is a clear source for that.

 

Anyway, that should be thought of as a statement about the interpretation and the implications of quantum mechanics in light of classical mechanics. It is perfectly possible to have a good understanding of the mathematical framework and how to use it.

My long background was waves (radio, acoustics, signal) before learning QM, that helped me a lot. Conceptually, more than for the maths.