Sabine Hossenfelder explains the most important and omnipresent ingredients of quantum mechanics: what is the wave-function and how do you calculate with it.

Much of what makes quantum mechanics difficult is really not the mathematics. In fact, quantum mechanics is one of the easier theories of physics. The mathematics is mostly just linear algebra: vectors, matrices, linear transformations, and so on. You’ve learned most of it in school already! However, the math of quantum mechanics looks funny because physicists use a weird notation, called the bra-ket notation. I tell you how this works, what it’s good for, and how to calculate with it.