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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):

  1. Largely focuses on non-relativistic quantum mechanics at the level of Sakurai/Ballentine. (Tinkham does this.)

  2. 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.)

  3. 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.)

  4. (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.

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  • $\begingroup$ I like the books by Isham. The QM book is really nice, and I like the book on groups and vector spaces too. Perhaps it is worth to take a look, although the latter really is only an introduction (roughly 50 pages on group theory, 50 pages on vector spaces and 50 pages on group representations). It has some examples from QM, but I don't think it is especially tied to it. $\endgroup$
    – Tobias Fünke
    Commented Apr 3, 2023 at 16:22
  • $\begingroup$ A more rigorous and throughout book would be Peter Woit's: "Quantum Theory, Groups and Representations" - a PDF can be found here, but I don't know it enough to recommend it, although the author is well-known. $\endgroup$
    – Tobias Fünke
    Commented Apr 3, 2023 at 16:25
  • $\begingroup$ Thank you @TobiasFünke I will take a look at Isham, though it seems like it's just focused on the group/vector space theory which I already (somewhat) know rather than the connection to the physics. Woit I believe may be a bit too long and not quite a companion so much as a next book in QM! $\endgroup$
    – EE18
    Commented Apr 3, 2023 at 16:45
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/6108/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Apr 3, 2023 at 18:12
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    $\begingroup$ The hbar chat on this site has some folks , I think, who enjoy discussing representation theory in QM :). $\endgroup$
    – Silly Goose
    Commented Apr 3, 2023 at 18:45

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