Lecturer: Gianfausto Dell'Antonio
schedule: room A-136, Tuesday 14-16, Friday 9-11
start: Friday 17 October 2014
Table of contents:
- "Wave mechanics" (de Broglie, Schrödinger) and
"matrix mechanics" (Born, Heisenberg, Jordan). Analogy with Classical
Mechanics (Dirac, Pauli).
- Axioms: states and observables (Schroedinger, Heisenberg, von
Neumann); measurement. Difficulties: hidden variables? Bell's
inequalities. Alternative theories.
- Construction of kinematics and dynamics. Maps of states. Automorphisms of observables. Unitary dynamics. Generators.
- Analogy with Hamiltonian dynamics. The problem of quantisation.
- Operators in a Hilbert space. Quadratic forms (basic facts). An
example: analytic solution for the free motion. Propagation
inequalities. Quadratic (Dirichlet) form for free motion on a line.
Berry phase, adiabatic limit.
- Elements of C*-algebras. Dynamical systems. GNS representation. An example: systems on a lattice. KMS condition.
- Quantisation: Weyl's system, Weyl's algebra. Second quantisation. Representations (Bargmann-Segal, Fock, Berezin)
- Semi-classical limit. Stationary and non-stationary WKB method.
Pre-requisites: basics of Quantum
Mechanics (familiarity not requried).
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).