CODE  90697 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/07 
TEACHING LOCATION 

SEMESTER  2° Semester 
TEACHING MATERIALS  AULAWEB 
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.
Starting from few basic concepts from quantum mechanics, which will be recalled in the first lectures, the student will learn the tools that play a crucial role in the formalization of quantum mechanics as a rigorous mathematical theory. In order to pursue this goal, the student will
With these results the student acquires the ability to switch from an abstract algebraic approach to a more concrete one, based on the theory of operators on a Hilbert space, thus clarifying the relation with the traditional description of quantum mechanics. More specifically, the student will learn how to
Towards the end of the course, in order to deal with applications to concrete problems of physical interest, the student will explore some tools from the theory of unbounded selfadjoint operators on Hilbert spaces.
Taught class.
Preliminary physical observations
Algebraic description of a physical system
Quantum systems and noncommutativity
Quantum particle
Schrödinger equation
Examples and applications
Lecture notes, as well as additional references, will be made available during the course.
Office hours: By appointment.
MARCO BENINI (President)
PIERRE OLIVIER MARTINETTI
CLAUDIO BARTOCCI (President Substitute)
NICOLA PINAMONTI (President Substitute)
All class schedules are posted on the EasyAcademy portal.
The exam consists of an oral test, during which the student is asked to demonstrate familiarity with the concepts and the tools presented during the lectures. The exam aims at testing the student's ability to state the definitions and the theorems exhamined throughout the course and to reproduce their proofs autonomously.
The exam consists of an oral test. Please get in touch with the lecturer in order to schedule an appointment.
Students with a certified learning disorder, disability or other special educational needs are advised to contact the lecturer at the beginning of the course in order to agree on teaching and examination methods that, in compliance with the teaching objectives, take into account individual learning methods and provide appropriate compensatory tools.