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I want to understand spherical harmonics. I want to really grok them deeply. I want to be able to visualize them and understand them.

I'm the sort who can't take anything on faith, especially where quantum mechanics is concerned. So I want to understand angular momentum so I can really see what spin 1/2 means in contrast. I need to see the craziness proven.

What should I know, to learn this? What should I read? I consider myself fairly capable with calculus and differential equations. I've taken several more math classes. I've worked nearly all the problems in the first five chapters of Bransden and Joachain's Introduction to Quantum Mechanics, and more than half in the angular momentum chapter, but I am greatly dissatisfied.

I have tried Arfken and Weber, and got a bit overloaded, but I will try that book again. I am also looking at Fourier Series and Orthogonal Functions by Harry F. Davis. Do people have other sources that they prefer?

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# To understand how spherical harmonics apply to integer spin but not half integer spin

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