The best way to learn quantum mechanics is to think more, associate more, and don't dwell on mathematics.
Learning quantum mechanics well requires two things:
1. Master the mathematical tools used to describe quantum mechanics.
2. Understand the thinking method of describing physical system with quantum mechanics.
The mathematical tools needed to learn quantum mechanics well are as follows:
1. Some basic knowledge of mathematical analysis, including basic real variable functions, complex variable functions, ordinary differential and partial differential equations, etc. I think these will be involved in any advanced mathematics or mathematical analysis course of science.
2. Understand some basic special functions, such as spherical harmonic function and Bessel function. These will be introduced in the course of mathematical physics methods offered by the physics department, and of course you don't have to look them up yourself.
3. Have a good understanding of the basic concepts of linear algebra, including linear space, subspace, orthogonality, basis, matrix and linear transformation, eigenvalue and eigenvector. In particular, it is necessary to establish the concept that matrix is transformation and eigenvector is transformation into basis, because this is the basis of describing quantum mechanics. These concepts should also be clearly established in the undergraduate course of linear algebra.
4. It is better to have a little group theory foundation, which is helpful to understand symmetry.
The above are the mathematical tools that need to be mastered in learning quantum mechanics. Because it seems to be your difficulty, I spent more pen and ink. After mastering these basic mathematical tools, learning quantum mechanics is the process of understanding its physical thoughts, that is, the method of describing physical systems with operators and states. There are several suggestions for this:
Find a good textbook. If you are a physics major, I don't recommend Zeng Jinyan's Quantum Mechanics Course (let alone his problem set) and Cheng Tansheng's Modern Quantum Mechanics Course. I recommend Modern Quantum Mechanics by Sakurai, especially the first three chapters. Starting from the thinking mode of quantum mechanics, a series of thinking trajectories of physical quantities are derived, which is very wonderful.