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.
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by Gianfausto Dell'Antonio - Sissa, Trieste
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.
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 Ingemar Bengtsson - Stockholms universitet, Fysikum
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.
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.