OVERVIEW

The course intends to provide a first part of complementary mathematical methods of physics aimed at the study of the elements of quantum mechanics and a second part aimed at an introduction to quantum mechanics. Particular emphasis will be placed on the common features of classical wave theory and wave mechanics, on the discussion of experiments and on the solution of simple problems.

AIMS AND CONTENT

LEARNING OUTCOMES

The first objective of the teaching is to complete the two-year mathematical training, providing the basic tools of Fourier analysis. To do this we will make use of concrete physical examples, such as oscillating systems and waves in dispersive and non-dispersive media. This objective is preparatory to the second:  to provide the basic elements of single particle wave mechanics (from the de Broglie hypothesis to the study of the Schroedinger equation in simple cases such as holes, harmonic oscillator, hydrogen atom) with some notes on systems multiparticle quantum physics.

AIMS AND LEARNING OUTCOMES

The aim of the course is to bring students to a good level of knowledge of the basic principles of modern physics.The student is expected to be able to apply  mathematical techniques such as Fourier series and  Fourier integrals  to the resolution of modern physics problems.The course has as its main objective the acquisition of basic knowledge and skills relating to advanced mathematical tools that have general applications in Physics. Particular attention is given to the understanding of the arguments, the rigor in the presentation of concepts and reasoning, and the application aspects of the theoretical tools developed.

PREREQUISITES

First year general mathematics and physics courses.

TEACHING METHODS

Both lessons and exercises are carried out on the blackboard. Students are always invited to actively participate by asking questions and proposing solutions to the proposed problems. The active involvement of students probably contributes to reducing the time and difficulties associated with studying the topics presented in the course.

SYLLABUS/CONTENT

Mathematical Methods
Reviews of complex algebra and algebra, Hermitian matrices and their diagonalization; Eigenvectors and eigenvalues ​​and their use in classical physics: principal axes of inertia and small oscillations. Notes on Fourier analysis and its applications.Free harmonic oscillations, normal modes. Wave propagation of physical disturbances. Elastic waves. D'Alembert equation. Standing waves and vibrating string. Local conservation laws and continuity equation. Plane and spherical waves. Wave packets and Fourier analysis.Dispersive means. Phase velocity and group velocity. Dispersion relations and wave equations.
Elements of quantum mechanics
Crisis elements of classical theories: black body, photoelectric effect. Electromagnetic field in a cavity as a set of independent oscillators. Einstein's hypothesis E= h nu . De Broglie's hypothesis mv= h /lambda and its experimental verification (Davidson and Germer experiment and recent experiments on interference of material waves). Basic concepts of quantum mechanics: time-dependent Schroedinger equation, wave function and quantum state. Continuity equation and probabilistic interpretation of the wave function. Uncertainty principle. Correspondence rules. Classical Hamilton function and quantum Hamilton operator. Stationary states and time-independent Schroedinger equation. Free states and bound states. Gaussian packets. Schroedinger equation with potential, study of some one-dimensional cases: wells, potential barriers and harmonic oscillator. Calculation of the average energy of a quantum harmonic oscillator in contact with a thermostat. The Schroedinger equation in three dimensions. Infinite cubic potential well and the notion of degeneracy of levels. The Hydrogen atom: levels and quantum numbers. The Stern-Gerlach experiment and spin. Notes on quantum mechanics of multiparticle systems. Bosons and Fermions. Entanglement.

RECOMMENDED READING/BIBLIOGRAPHY

-Notes provided by the teacher (for the mathematical methods part)
-  Physical Chemistry, Peter Atkins and Julio De Paula, (Zanichelli 2012);
- Introduction to Quantum Mechanics: David J. Griffiths (Benjamin Cumming, 2004);
- Feynman's physics, Volume 3. “Quantum mechanics” (Zanichelli 2007); also available online in English for free: http://www.feynmanlectures.info/

TEACHERS AND EXAM BOARD

Exam Board

PIERANTONIO ZANGHI' (President)

PAOLO SOLINAS

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of a written test and an interview. The written test consists of some problems that cover a large part of the course contents.The student is then given the freedom to choose between two types of oral exam: a shorter oral exam, aimed at consolidating the grade obtained in the written exam, and a longer oral exam in which the change in grade can be significant. This method is used to allow the student, aware of having achieved a good preparation, to be able to make up for any shortcomings in the written test.

ASSESSMENT METHODS

The written test is aimed at verifying the ability to solve specific problems similar to those discussed in the course, but original. The difficulty of the test is graduated, so that it is possible to separate the assessment of elementary basic knowledge, sufficient to pass the test, from the assessment of more advanced skills. In both the short and long forms of the oral exam, we always start from the written test, in order to ascertain the types of errors, the student's real mastery of the skills required on the theoretical topics of the written test and to highlight any potential lack of preparation. In the long oral exam we continue with the assessment of skills on other topics covered during the course. In both cases, the exam is aimed at ascertaining the degree of achievement of the training objectives, in a graduated form. In both cases, particular attention is dedicated to ensuring that the student has acquired a good level of knowledge of the basic principles of modern physics and is able to apply the mathematical techniques carried out in the course to the resolution of modern physics problems.

Exam schedule

FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.