The discussion revolves around recommendations for books on ordinary differential equations (ODEs) with applications, particularly in the context of preparing for a quantum mechanics course. Participants explore the necessary mathematical background, including ODEs, linear algebra, and potentially partial differential equations (PDEs).
Participants express differing views on the importance of ODEs versus PDEs for quantum mechanics, and there is no consensus on the specific mathematical prerequisites needed beyond ODEs.
Some participants note that the mathematics course prerequisite for quantum mechanics does not include PDEs, leading to uncertainty about whether these will be adequately covered in the quantum mechanics course itself.
Thank you! Do you know if there is anything else needed for Quantum Mechanics that I should also learn before taking the course?axmls said:Try "Mathematical Methods in the Physical Sciences" by Mary Boas. It's doesn't cover only DEs, but it's got some of everything (at an undergrad level). If you have no exposure to differential equations, you should probably focus on just a differential equations textbook without worrying if it's extremely focused on applications.
I'm of the opinion that you should be comfortable with the math needed in a course before the course starts, because it's a whole lot easier to learn the physics behind something than it is to learn the physics behind something while simultaneously trying to learn the language it's represented in. So I'd say any differential equations textbook would do.
Any differential equations techniques that are needed in quantum mechanics that aren't covered in many DE textbooks will likely be covered in the quantum mechanics textbook anyway.
To be more specific, do you mean having a strong background on eigenvalue problems and matrix operations or do I need more? Also, what about Fourier analysis(and Fourier integrals)?axmls said:If it's a full course on quantum mechanics, it wouldn't hurt to get some background in linear algebra if your linear algebra isn't strong.
The mathematics course that is a prerequisite to the quantum mechanics course does not include partial differential equations, so I expect the professor of the QM course to teach us the basic techniques that will be used in his course.mpresic said:You probably need more partial differential equations rather than differential equations