I know this question has been asked a million times and I have looked at the various questions/answers, but am yet to find a perfect solution. At one of the suggestions here, I picked up the book by Tinkham but it just feels too sloppy to understand what's going on.
I am looking for a textbook on group theory and quantum mechanics which does the following (and perhaps it doesn't exist):
Largely focuses on non-relativistic quantum mechanics at the level of Sakurai/Ballentine. (Tinkham does this.)
Uses modern mathematical notation/structures other than, perhaps, using Dirac notation for the underlying vector space of the representation. (Tinkham doesn't talk about sets even naively, homomorphisms as maps, etc.)
Gives a somewhat self-contained introduction to the relevant group theory -- this is less crucial as I have some background but the point here is that I don't want it jumping to the level of the book by Hall, for example. (Tinkham presupposes a lot of (admittedly elementary) facts which I only caught because I have some modest background myself, at the level of Szkeres's A Course in Modern Mathematical Physics.)
(Not mandatory) Is reasonably small, and can be read as a companion to Ballentine/Sakurai in order to make rigorous the developments which are sometimes somewhat opaque (e.g. angular momentum).
Perhaps such a book does not exist but I figured there would be no better place to ask than right here.
