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Self-adjoint operators in quantum mechanics

Lecturer: 
Matteo Gallone
Course Type: 
PhD Course
Anno (LM): 
First Year
Academic Year: 
2023-2024
Period: 
October-November
Duration: 
20 h
Description: 

The course will give an overview on the operator-theoretical tools needed for a rigorous formalization and treatment of a quantum mechanical model with special emphasis on unbounded self-adjoint operators.

Topics:

  1. Axioms of Quantum Mechanics, the need for unboundedness and self-adjointness;
  2. General theory of unbounded operators on Hilbert spaces (closable, closed, symmetric, adjoint, self-adjoint) and their spectra.
  3. Spectral theorem and functional calculus
  4. Unitary time evolution and Stone's theorem. Well-posedness of abstract Schroedinger, Heat and Wave equations
  5. Self-adjoint extensions: Krein-Vishik-Birman theory and the rigorous definition of point interactions in 3 spatial dimensions.

 

Research Group: 
Geometry and Mathematical Physics
Next Lectures: 

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