Quantum Theory, Groups and Representations: An Introduction
by Peter Woit
Publisher: Columbia University 2014
Number of pages: 396
These notes 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. The approach to this material is simultaneously rather advanced, using crucially some fundamental mathematical structures normally only discussed in graduate mathematics courses, while at the same time trying to do this in as elementary terms as possible.
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by S. Gustafson, I.M. Sigal - University of Toronto
These lectures cover a one term course taken by a mixed group of students specializing either in mathematics or physics. We illustrate an interplay of ideas from various fields of mathematics, such as operator theory, differential equations, etc.
by Roman Schmied - arXiv.org
This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be analyzed and understood at a deeper level than what is possible with more abstract representations.
by Jan Govaerts - arXiv
A basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract algebraic aspects of quantization.
by Gianfausto Dell'Antonio - Sissa, Trieste
The theory which is presented here is Quantum Mechanics as formulated in its essential parts on one hand by de Broglie and Schroedinger and on the other by Born, Heisenberg and Jordan with important contributions by Dirac and Pauli.