e-books in Mathematical Methods of Quantum Physics category
Lectures on Quantum Mechanics for Mathematiciansby Alexander Komech - arXiv.org , 2019
The main goal of these lectures is introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary orbits ...
(4205 views)
Using Mathematica for Quantum Mechanics: A Student's Manualby Roman Schmied - arXiv.org , 2019
This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be analyzed and understood at a deeper level than what is possible with more abstract representations.
(5197 views)
Homological Tools for the Quantum Mechanicby Tom Mainiero - arXiv.org , 2019
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.
(4334 views)
Uncertainty and Exclusion Principles in Quantum Mechanicsby Douglas Lundholm - arXiv.org , 2018
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.
(5074 views)
Mathematical Concepts of Quantum Mechanicsby S. Gustafson, I.M. Sigal - University of Toronto , 2001
These lectures cover a one term course taken by a mixed group of students specializing either in mathematics or physics. We illustrate an interplay of ideas from various fields of mathematics, such as operator theory, differential equations, etc.
(7187 views)
Mathematical Foundations of Quantum Mechanicsby Valter Moretti - arXiv , 2015
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 ...
(8407 views)
Quantum Theory, Groups and Representations: An Introductionby 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...
(9367 views)
Numerical Methods in Quantum Mechanicsby 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.
(8246 views)
A Short Introduction to the Quantum Formalismby 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.
(8265 views)
Mathematical Tools of Quantum Mechanicsby 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.
(10999 views)
Quantization and Semiclassicsby 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.
(7740 views)
Symplectic Geometry of Quantum Noiseby 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.
(9925 views)
An Introduction to Microlocal Analysisby 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.
(11294 views)
Lecture notes on C*-algebras, Hilbert C*-modules, and quantum mechanicsby 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.
(13410 views)
A Pedestrian Introduction to the Mathematical Concepts of Quantum Physicsby 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.
(14579 views)
Geometry of Quantum Mechanicsby 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.
(14440 views)
Mathematical Methods in Quantum Mechanicsby 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.
(16150 views)
Guide to Mathematical Concepts of Quantum Theoryby 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.
(12785 views)