Arnold Neumaier & Dennis Westra 
Quantum Mechanics via Lie Algebras [PDF ebook] 

This monograph introduces mathematicians, physicists, and engineers to the ideas relating quantum mechanics and symmetries — both described in terms of Lie algebras and Lie groups. The exposition of quantum mechanics from this point of view reveals that classical mechanics and quantum mechanics are very much alike. Written by a mathematician and a physicist, this book is (like a math book) about precise concepts and exact results in classical mechanics and quantum mechanics, but motivated and discussed (like a physics book) in terms of their physical meaning. The reader can focus on the simplicity and beauty of theoretical physics, without getting lost in a jungle of techniques for estimating or calculating quantities of interest.