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Mathematical Methods of Quantum Physics
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Quantum Theory, Groups and Representations: An Introduction
by Peter Woit - Columbia University , 2014
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...
Numerical Methods in Quantum Mechanics
by Paolo Giannozzi - University of Udine , 2013
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.
A Short Introduction to the Quantum Formalism
by Francois David - arXiv , 2012
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.
Mathematical Tools of Quantum Mechanics
by Gianfausto Dell'Antonio - Sissa, Trieste , 2012
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.
Quantization and Semiclassics
by Max Lein - arXiv , 2010
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.
Symplectic Geometry of Quantum Noise
by Leonid Polterovich - arXiv , 2012
We discuss a quantum counterpart of certain constraints on Poisson brackets coming from 'hard' symplectic geometry. They can be interpreted in terms of the quantum noise of observables and their joint measurements in operational quantum mechanics.
An Introduction to Microlocal Analysis
by Richard B. Melrose, Gunther Uhlmann - MIT , 2008
The origin of scattering theory is the study of quantum mechanical systems. The scattering theory for perturbations of the flat Laplacian is discussed with the approach via the solution of the Cauchy problem for the corresponding perturbed equation.
Lecture notes on C*-algebras, Hilbert C*-modules, and quantum mechanics
by N.P. Landsman - arXiv , 1998
A graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space localization.
A Pedestrian Introduction to the Mathematical Concepts of Quantum Physics
by Jan Govaerts - arXiv , 2008
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.
Geometry of Quantum Mechanics
by Ingemar Bengtsson - Stockholms universitet, Fysikum , 1998
These are the lecture notes from a graduate course in the geometry of quantum mechanics. The idea was to introduce the mathematics in its own right, but not to introduce anything that is not directly relevant to the subject.
Mathematical Methods in Quantum Mechanics
by Gerald Teschl - American Mathematical Society , 2009
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.
Von Neumann Algebras and Local Quantum Theory
by I. F. Wilde , 2009
These notes are based on lectures given many years ago at the Institute of Physics, University of Sao Paulo, Brazil. The material includes an introduction to von Neumann algebras and modular theory and the beginnings of algebraic quantum theory.
Guide to Mathematical Concepts of Quantum Theory
by Teiko Heinosaari, Mario Ziman - arXiv , 2008
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.