Conceptual and Mathematical Foundations of Quantum Mechanics
(graduate course, SISSA -- November 2015 - February 2016)

Lecturer: Gianfausto Dell'Antonio

venue and schedule: room A-136, Mo + Wed, 9-11 am
start: Monday 12 October 2015
end: Wednesday 11 November 2015
duration: 20 hours (1 cycle)

Tentative contents of the 10 lectures:
  1. Historical remarks. De Broglie, Schrödinger, Born-Heisenberg-Jordan. Axioms (states and observables).
  2. Difficulties (decoherence, measurement). Bell’s inequalities. Alternative theories.
  3. Mapping of states. Homeomorphism of observables. Theorems of Wigner, Kadison, Segal.
  4. Continuity. One-parameter groups of unitary operators. Comparison with Hamiltonian dynamics.
  5. Operators in Hilbert spaces. Basic facts.
  6. Analytic solution of free motion. Propagation inequalities. Wave operators.
  7. Elements of C*-algebras. GNS representation. Automorphisms.
  8. The problem of Quantization. Weyl system. Weyl algebra. Representations of Weyl and Berezin.
  9. Wigner functions. Pseudo-differential operators. Born-Sommerfeld quantization.
  10. Conditioning and dilations. Markov approximation. Quantum dynamical semigroups.

Pre-requisites: Any general master-level education in Maths or Physics and an introductory  (undergraduate-like) exposition to Quantum Mechanics (the course is meant to start "from scratch").

Literature: G. Dell'Antonio, Lectures on the Mathematics of Quantum Mechanics I (2015)
Italian version:
G. Dell'Antonio, Mathematical Aspects of Quantum Mechanics. Volume 1 (2011).