Guide to Mathematical Concepts of Quantum Theory
by Teiko Heinosaari, Mario Ziman
Publisher: arXiv 2008
Number of pages: 188
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper the authors introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory.
Home page url
Download or read it online for free here:
by Gerald Teschl - American Mathematical Society
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.
by S. Gustafson, I.M. Sigal - University of Toronto
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.
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.
by Valter Moretti - arXiv
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 ...