Lecturer: Gianfausto Dell'Antonio
schedule: room A-136, Mo + Wed, 9-11 am
end: Wednesday 11 November 2015
duration: 20 hours (1
Tentative contents of
the 10 lectures:
- Historical remarks. De Broglie, Schrödinger,
Born-Heisenberg-Jordan. Axioms (states and observables).
- Difficulties (decoherence, measurement). Bell’s
inequalities. Alternative theories.
- Mapping of states. Homeomorphism of observables.
Theorems of Wigner, Kadison, Segal.
- Continuity. One-parameter groups of unitary operators.
Comparison with Hamiltonian dynamics.
- Operators in Hilbert spaces. Basic facts.
- Analytic solution of free motion. Propagation
inequalities. Wave operators.
- Elements of C*-algebras. GNS representation.
- The problem of Quantization. Weyl system. Weyl
algebra. Representations of Weyl and Berezin.
- Wigner functions. Pseudo-differential operators.
- Conditioning and dilations. Markov approximation.
Quantum dynamical semigroups.
general master-level education in Maths or Physics and an
introductory (undergraduate-like) exposition to Quantum Mechanics
(the course is
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).