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Mathematical Methods of Quantum Mechanics

Algebraic Methods for Quantum Theories

- introduction to the theory of C*-algebras and von Neumann algebras
- representations
- automorphisms and dynamical systems
- KMS condition
- contraction semigroups
- algebraic formulation of Quantum Mechanics and Statistical Mechanics
- elements on the algebraic and the constructive Quantum Field Theory

FIR consolidator grant "Cond-Math: Condensed Matter in Mathematical Physics"

Research topics: many-body quantum systems, Schrödinger operators, Bose-Einstein condensation, non-linear Schrödinger equations, variational methods in mathematical physics, singular perturbations of Schrödinger operators

Quantum Mechanics

  • scratch course of spectral theory of operators on Hilbert spaces
  • a reminder of classical probability
  • fundamental postulates of quantum physics
  • Heisenberg uncertainty principle
  • the von Neumann-Lüders postulate, and the issue of individual states
  • symmetries and the Wigner-Kadison theorem
  • symmetry groups
  • projective representations
  • eliminability of multipliers for one parameter groups
  • Weyl relations
  • von Neumann uniqueness
  • CCR and uncertainties


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