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 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 Max Lein - arXiv
This text is aimed at graduate students in physics in mathematics and designed to give a comprehensive introduction to Weyl quantization and semiclassics via Egorov's theorem. An application of Weyl calculus to Born-Oppenheimer systems is discussed.
by Teiko Heinosaari, Mario Ziman - arXiv
In this text the authors introduce the quantum theory understood as a mathematical model describing quantum experiments. This is a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory.
by Douglas Lundholm - arXiv.org
These are lecture notes for a master-level course given at KTH, Stockholm, in the spring of 2017, with the primary aim of proving the stability of matter from first principles using modern mathematical methods in many-body quantum mechanics.