In this course the basic concepts of quantum mechanics will be presented, highlighting the mathematical techniques necessary for the rigorous 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 tools from operator theory and Hilbert space analysis 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 self-adjoint operators on Hilbert spaces.
Taught class.
Preliminary physical observations
Algebraic description of a physical system
Quantum systems and non-commutativity
Quantum particle
Schrödinger equation
Examples and applications
Lecture notes, as well as additional references, will be made available during the course.
Ricevimento: By appointment.
MARCO BENINI (President)
PIERRE OLIVIER MARTINETTI
CLAUDIO BARTOCCI (President Substitute)
NICOLA PINAMONTI (President Substitute)
SIMONE MURRO (Substitute)
Consult the calendar at https://corsi.unige.it/en/corsi/9011/studenti-orario
The exam consists of an oral test. The test is passed with a minimal result of 18/30. During the exam session students can schedule an appointment for an oral test by getting in touch directly with the lecturer.
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.
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.
