Wave Mechanics

Sommerfeld was one of the greatest theoretical-physics teachers of all time. Just look at the Nobel-prize winners' list and check, who is a pupil of Sommerfeld's. The six-volume set "Lectures on theoretical physics" immediately shows, how this comes about. It's simply very good. He gives precisely all the mathmatical steps in a derivation with utmost clarity. Nevertheless, it's not a simple read. In my opinion the best volume of the entire great set is Vol. 6 on partial differential equations of mathematical physics.

Of course, these books are pretty old (written in the 1940ies and 50ies) and thus not always up to date (e.g., he uses the "ict metric" for relativity or no Dirac δ distribution to define Green's functions although in fact he has invented this idea as early as around 1910). You should definitely have a look at Sommerfeld's text books but make sure to also have a look at more recent textbooks on the same subject. Of course, as far classical physics is concerned, there's not too much to be desired.