General Physics 3

A.Y. 2021/2022
Overall hours
FIS/01 FIS/02 FIS/03 FIS/04 FIS/05 FIS/06 FIS/07 FIS/08
Learning objectives
The course of General Physics 3 has the purpose of providing the basic concepts of relativity and quantum mechanics. Its goal is a review of the basic concepts of classical mechanics and of electromagnetism under the light shed by relativity and quantum physics with special attention to fundamental and unifying issues of the physics research such as the conservation laws, the symmetries and their physical meaning with some openings also to some recent findings.
Expected learning outcomes
Mastery of the subject matter of the program; basic knowledge of special relativity and quantum mechanics; capacity of analysis and synthesis that allow students to discuss in qualitative and quantitative ways the description of some essential aspects of the physical description of our universe.
Course syllabus and organization

Single session

Lesson period
Second semester
More specific information on the delivery modes of training activities for academic year 2021/22 will be provided over the coming months, based on the evolution of the public health situation
Course syllabus
The theory of relativity and quantum mechanics constitute the conceptual basis of the modern view of the physical world. Their knowledge has fundamentally changed both our representation of the world and the role we have in it. Since they concern the notions of space, time, interaction, and the intrinsic meaning of object and of physical law, these theories, should be a part, at least in their essential aspects, of the cultural heritage of every person interested in science. Moreover, their great formal and conceptual elegance is a prime example of the explanatory power of mathematics in physics.

The course, starting from the conceptual difficulties arising from the impossible coexistence of electromagnetism with classical mechanics, has as its objective the introduction to special relativity and quantum mechanics with special attention to their physical meaning and their vast conceptual implications. When appropriate and / or possible, experiments will also be made and the reading of famous passages taken from the literature will be done.
Few insights on some current problems in the physical research will also be provided.

Special Relativity: Maxwell's equations and their non-invariance under Galilean transformations. The vector potential. What is a physical law. Requests for invariance under the Euclidean and under the Galileo groups. The notions of space and time. Space-time.
The principle of relativity. Assumptions underlying the Lorentz transformations. Lorentz transformations. The relative nature of simultaneity. Length contraction and time dilation. Addition of velocities. Minkowski space-time. Scalar, contravariant and covariant vectors, controvariant and covariant tensors. Four-velocity and four-momentum, relativistic energy. First elements of relativistic dynamics: the four-force and four-acceleration. Relativistic Doppler effect and relativistic beaming. Relativistic formalism for electromagnetism.

Quantum mechanics
Some experimental results of matter optics. Scalar wave equation for matter beams. Non-relativistic approximation. Some experimental facts: quantized interaction. The Schrödinger equation. Einstein and de Broglie relations. Statistical interpretation of the wavefunction. Introduction of the notion of observable. Ehrenfest equation. Heisenberg's uncertainty relations. Applications of Schroedinger equation in one dimension. Finite dimensional quantum systems. Bell inequalities. States, observables and the general formalism of quantum mechanics.
Prerequisites for admission
Skills aquired in the course on mathematical analysis and general physics.
Teaching methods
Lectures and exercises
Teaching Resources
Gasperini M. Manuale di Relatività Ristretta, Springer-Verlag Milan 2010
Rindler W. Introduction to Special Relativity, Oxford University Press, 1991.
F. Schwabl, Quantum Mechanics, Springer, 2007
C. J. Isham, Lectures on Quantum Theory, Imperial College Press, 2004
Lecture notes "Quantum mechanics: a first involvement" available on the websites below
Other infos:
Assessment methods and Criteria
The final examination consists of three parts: a written exam and an oral exam.

- During the written exam, the student must solve some exercises, with the aim of assessing the student's ability to solve problems in quantum mechanics and special relativity. The duration of the written exam will be proportional to the number of exercises assigned, also taking into account the nature and complexity of the exercises themselves (however, the duration will not exceed three hours).
- The oral exam can be taken only if the written component has been successfully passed. In the oral exam, the student will be required to illustrate results presented during the course and will be required to solve problems regarding quantum mechanics and special relativity in order to evaluate her/his knowledge and comprehension of the arguments covered as well as the capacity to apply them.

The complete final examination is passed if all parts (written, oral) are successfully passed. Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 0
FIS/03 - PHYSICS OF MATTER - University credits: 0
FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS - University credits: 0
FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 0
FIS/07 - APPLIED PHYSICS - University credits: 0
Practicals: 48 hours
Lessons: 45 hours
Educational website(s)
Friday 11-13 or simply on demand
Office - Virtual Room