
Lecturer: Gianfausto Dell'Antonio
venue and
schedule: room A136, Mo + Wed, 911 am
start: Monday
12 October
2015
end: Wednesday 11 November 2015
duration: 20 hours (1
cycle)
Tentative contents of
the 10 lectures:
 Historical remarks. De Broglie, Schrödinger,
BornHeisenbergJordan. Axioms (states and observables).
 Difficulties (decoherence, measurement). Bell’s
inequalities. Alternative theories.
 Mapping of states. Homeomorphism of observables.
Theorems of Wigner, Kadison, Segal.
 Continuity. Oneparameter 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.
Automorphisms.
 The problem of Quantization. Weyl system. Weyl
algebra. Representations of Weyl and Berezin.
 Wigner functions. Pseudodifferential operators.
BornSommerfeld quantization.
 Conditioning and dilations. Markov approximation.
Quantum dynamical semigroups.
Prerequisites: Any
general masterlevel education in Maths or Physics and an
introductory (undergraduatelike) 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). 
