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.
Home page url
Download or read it online for free here:
by Teiko Heinosaari, Mario Ziman - arXiv
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.
by Peter Woit - Columbia University
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...
by Richard B. Melrose, Gunther Uhlmann - MIT
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.
by Leonid Polterovich - arXiv
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.