Mathematical Concepts of Quantum Mechanics
by S. Gustafson, I.M. Sigal
Publisher: University of Toronto 2001
Number of pages: 185
These lectures cover a one term course taken by a mixed group of students specializing either in mathematics or physics. We decided to select material which illustrates an interplay of ideas from various fields of mathematics, such as operator theory, probability, differential equations, and differential geometry.
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by Paolo Giannozzi - University of Udine
The aim of these lecture notes is to provide an introduction to methods and techniques used in the numerical solution of simple (non-relativistic) quantum-mechanical problems, with special emphasis on atomic and condensed-matter physics.
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.
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 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.