First of all, you need to prepare the basic knowledge about functions in advanced mathematics courses (such as the basic knowledge of calculus, partial derivatives of multivariate functions, etc.). ) and the knowledge about how electrons move around atoms in college physics courses (this is a popular saying).

Then there are two most important mathematical tools in quantum physics, one is to solve partial differential equations and the other is linear algebra.

The knowledge of partial differential equations is mainly used in solving the wave function of the basic part of quantum physics. You can learn relevant knowledge by studying courses such as mathematical and physical methods.

Linear algebra is simply the algebraic operation of vectors, but unlike high school vectors, high school generally only learns plane (two-dimensional) or space (three-dimensional) vectors, while linear algebra extends it to learning N-dimensional vectors. Linear algebra is mainly used for the analysis of later quantum states, and related knowledge can be obtained by studying the course of linear algebra.

Summary:

The college courses you want to study are: advanced mathematics, linear algebra, college physics, mathematical physics methods.

The specific knowledge you want to learn is: calculus of functions, multivariate functions, partial differential equations, atomic energy bands, linear algebra.