- Docente: Davide Pastorello
- Credits: 6
- SSD: MAT/07
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Feb 21, 2024 to May 30, 2024
Learning outcomes
At the end of the course the student gets acquainted with some of the modern mathematical techniques used in quantum mechanics, such as abstract spectral theory, semiclassical pseudodifferential calculus, microlocalization. He is able to apply them in order to study typical phenomena in quantum mechanics, such as the tunnel effect and quantum resonances.
Course contents
-) General introduction to quantum phenomenology and the elementary formalism in finite dimension.
-) Definition and characterization of quantum observables and quantum states in infinite-dimensional Hilbert space by means of abstract spectral theory.
-) Uncertainty principle.
-) Non-boolean logic of quantum mechanics, states as generalized probability measures and Gleason’s theorem.
-) Von Neumann algebras and superselection rules.
-) Quantum symmetries in terms of unitary projective representations of groups, Wigner and Kadison theorems.
-) Overview about the abstract algebraic formulation of quantum theories.
Readings/Bibliography
Main references:
-) J. von Neumann. Mathematical foundations of Quantum Mechanics (Princeton University Press)
-) V. Moretti. Spectral Theory and Quantum Mechanics (Springer)
-) F. Strocchi. An Introduction to the Mathematical Structure of Quantum Mechanics (World Scientific)
Teaching methods
Classroom lectures
Assessment methods
Oral examination
Office hours
See the website of Davide Pastorello