Mathematical Tools of Quantum Mechanics
by Gianfausto Dell'Antonio
Publisher: Sissa, Trieste 2012
The author gives a presentation which, while preserving mathematical rigor, insists on the conceptual aspects and on the unity of Quantum Mechanics. 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.
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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 Tom Mainiero - arXiv.org
This paper is an introduction to work motivated by the question 'can multipartite entanglement be detected by homological algebra?' We introduce cochain complexes associated to multipartite density states whose cohomology detects factorizability.
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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.
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