TITLE: Resource for learning quantum mechanics from the viewpoint of representation theory
QUESTION [11 upvotes]: Quantum mechanics is deeply connected with representation theory. Therefore, I'm looking for a textbook or article which presents quantum mechanics in a representation theoretic manner. Could anyone provide me a reference to such a resource? I don't care if it's a math or physics book as long as it makes use of the language of representation theory mathematicians are familiar with.

REPLY [2 votes]: There is an upcoming book of Peter Woit, available for download if you click on the link. From the Preface:

These are the course notes prepared for a class taught at Columbia during the 2012-13 academic year. The intent was to cover the basics of quantum mechanics, from a point of view emphasizing the role of unitary representations of Lie groups in the foundations of the subject. [..]

I just noticed that these lecture notes were also mentioned in the comments.