LEARNING OUTCOMES

In this course will be presented the basic concepts of quantum mechanics, highlighting the mathematical techniques necessary for the strict formalization of this theory. In particular, the algebraic structure of quantum observables will be studied and the theorems necessary for the representation of this algebra will be analyzed. Finally, some instruments of operator theory and analysis of Hilbert spaces will be used to derive the evolution equations of Schrödinger and Heisenberg and to discuss their solutions.

TEACHING METHODS

Teaching style: In presence

SYLLABUS/CONTENT

TO BE UPDATED

General relativity

• Varietà differenziabili pseudo-riemanniane e campi vettoriali.
• Curvatura, trasporto parallelo e geodetiche.
• Equazioni di Einstein: loro soluzioni in casi particolari.

Introduction to quantum theories

• Basic concepts of quantum mechanics: measuremnts, observables, states.
• Observables algebra. GNS Theorem and formulation of quantum mechancis on Hilbert spaces.
• Automorphisms describing time evolution. Schrödinger and Heisenberg equations and properties of their generator. Theory of unbounded selfadjoint operators.