A Pedestrian Introduction to the Mathematical Concepts of Quantum Physics
by Jan Govaerts
Publisher: arXiv 2008
Number of pages: 79
These notes offer 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 in contrast to more standard treatments of such issues, while also bridging towards the path integral formulation of quantization.
Home page url
Download or read it online for free here:
by N.P. Landsman - arXiv
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.
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.
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.