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for instance right now I'm reading quantum mechanics by boas, and I see that bessel's functions are crucial in the solution of the schroedinger equation for the hydrogen atom, and it occurs to me that had this nifty little trick not been in the book I wouldn't have been able to see that that equation was soluable, and I also now lack any real knowledge of bessel's functions outside of the trick used in the book, so its not like I would see the solution in another problem that was similar as I have not grokked it yet.

I also saw in the library that there are over 2 dozen large books on the theory of bessel functions, so where would I be able to get the grit of the theory without having to read a massive book on the subject?

I'm planning on reading Boas over the summer however I also see the problem that when some concepts are introduced they seem very insignificant (the introduction to bessel's functions in my diff eq book being an example) that my brain doesn't see the need to spend time and grock that concept. So I have to ask when it was that other people here acquired the mathematical skill to study these problems and have a general idea of where the answer to them lies (whether or not they are entirely familiar with the subject or not).