What kind of differential equations one must know for QM?

[Joker93]

I will be taking a first course on Quantum Mechanics and just wanted to know what kind of ordinary differential equations must i know before going into the course. Thank you!

 

[S.G. Janssens]

As far as ODEs are concerned, boundary value problems for second order equations (in particular: Sturm-Liouville problems) come to mind. They often arise when studying systems in QM on a bounded spatial domain and applying a technique called "separation of variables".

However, my experience from when I was an undergraduate is that most first courses on QM will be quite gentle on the mathematics, introducing unknown mathematical concepts along the way. So there is no need to first read a book on boundary value problems before taking your QM course. If you find the mathematics by itself interesting, you can then choose to read more about it and people here can provide you with references.

 

[blue_leaf77]

Probably almost all differential equation problems in QM are encountered in the Schrödinger equation in position basis. The very first one you will most likely encounter in your course is a Helmholtz-type differential equation arising in infinite well problem. Others will be Hermite differential equation, Laguerre differential equation, and associated Legendre differential equation. Anyway, just read through the chapter on differential equation in your textbook, you will hardly miss those needed in QM.