Studying Sturm-Liouville Form: Finding Resources & Problem Sets

[Mordred]

I have been studying the Higg's field and ran across a particular equation that made me realize I need to better understand Sturm-Liuoville. So naturally I went looking through my differential calculus textbooks but was surprised they didn't cover this detail. While the article covers how to get to the Sturm-Liouville form in the following equation.

$$-p(\varphi\frac{d^2\overline{\phi}_n}{d\phi^2}-\acute{p}9\varphi\frac{d\overline{\phi}_n}{d\varphi}+q(\varphi)\overline{\phi}_n=\lambda_nw(\varphi)\overline{\phi}_n(\varphi)$$

I would much rather have a solid good resource so I can study Sturm-Liouville. Ideally one that has a good range of problem sets I can practice with. Particularly since its been over 15 years since I completed University.

However like a lot of things if you don't keep in practice one tends to forget lol

I did some google searching on the topic but would like to know if anyone has any recommendations.

 

[ShayanJ]

Arfken's "Mathematical methods for physicists" has a good chapter on SL theory.

 

[Mordred]

Perfect precisely the details I needed. I glanced through the ebook and liked the textbook so much I ordered a hardcopy thanks a bunch for the recommendation.

edit studying this textbook further it has provided me all the tools to work through the dissertation I am studying. Once again thanks