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 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 Gerald Teschl - American Mathematical Society
This is a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required.
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 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.