29209 - Modern Physics M

Course contents

The course is entirely taught by Prof. Fabio Ferrari and is structured into two main modules, covering some of the most groundbreaking revolutions in 20th-century physics:

Module 1: Special Relativity (32 hours)

A journey into the nature of space and time, starting from the Michelson-Morley experiment to the full formulation of Einstein’s theory. The module introduces the postulates of Special Relativity, with a focus on time dilation and length contraction, followed by an in-depth study of the Lorentz transformations, causality in relativity, and the transformation of velocity and acceleration. Key physical quantities such as relativistic momentum, energy, and mass are also covered. The module concludes with an analysis of Lorentz invariants and the four-momentum vector, essential tools in the modern description of relativistic phenomena.

Module 2: Quantum Mechanics and Nuclear & Subnuclear Physics (28 hours)

This module introduces the wave nature of matter and the foundations of Quantum Mechanics, beginning with interference phenomena (Young’s experiment) and the D'Alembert equation. Core topics include blackbody radiation, the photoelectric effect, the Compton effect, wave-particle duality, and De Broglie’s wavelength.
A central part of the module is dedicated to the Schrödinger equation, both in its general form and in the context of one-dimensional potentials (wells, barriers, and the tunneling effect). The module continues with atomic models, from Bohr’s atom to the hydrogen spectrum, and the quantum numbers that describe an electron’s state. It concludes with the Stern-Gerlach experiment, the basics of nuclear fission and fusion, and an introduction to elementary particle physics.

Each module includes guided problem-solving sessions, designed to strengthen understanding and apply theoretical concepts to real physical situations.

Readings/Bibliography

Lecture notes in LaTeX format are made available free of charge by the instructor.

Teaching methods

In-person lectures are delivered using a projected virtual whiteboard, complemented by slides and videos.

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Students with specific learning disorders (SLD) or temporary/permanent disabilities:

We recommend contacting the University Office responsible for support services in a timely manner (https://site.unibo.it/studenti-con-disabilita-e-dsa/it). The office will evaluate the students' needs and, where appropriate, propose possible accommodations. These must in any case be submitted for approval at least 15 days in advance to the course instructor, who will assess their suitability also in relation to the learning objectives of the course.

Assessment methods

The assessment consists of a written exam lasting 1 hour and 30 minutes, followed by an oral exam.

The written exam includes 8 exercises, each graded up to 4 points, for a total of 32 points. To be admitted to the oral exam, students must score at least 16 points in the written exam.

Students may take the oral exam in the same exam session as the written or in one of the following sessions.

The oral exam covers the entire course program and typically includes:

• one question on Special Relativity,

• one question on Quantum Mechanics,

• one question on Nuclear and Subnuclear Physics.

Teaching tools

The virtual whiteboard used during the lectures will be made available to all students for later consultation. Similarly, the slides and videos presented in class will be accessible to everyone for review and further study.

Office hours

See the website of Fabio Ferrari