Mathematical Methods in Quantum Mechanics
by Gerald Teschl
Publisher: American Mathematical Society 2009
Number of pages: 317
This book serves as 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.
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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 Valter Moretti - arXiv
The author reviews the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas ...
by Francois David - arXiv
These notes present an introductory, but hopefully coherent, view of the main formalizations of quantum mechanics, of their interrelations and of their common physical underpinnings: causality, reversibility and locality/separability.
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.