FOUNDATIONS OF Modern Physics

The aim of the course is to give an overview of modern physics as established at the end of the 19th and at the beginning of the 20th centuries, and mainly developed over the first decades of 1900: the special theory of relativity, which showed how the explanation of the experimental evidence already available at the time required the revision of the concepts of space and time; statistical mechanics, that gave impetus to the modern atomistic view of matter; quantum mechanics that revealed the wave-particle dualism. Finally, these constructions made it possible to understand the physics of atomic nuclei.

Physical theories will be presented in terms of logical, mathematical structure and experimental evidence.

At the end of the course, the student will have acquired inductive and deductive reasoning skills, will be able to critically tackle the topics studied. The student will apply the scientific method to the study of natural phenomena and will be able to critically evaluate similarities and differences between physical systems and the methodologies to be used. Furthermore, he/she will be able to expose the topics of modern physics covered by the course appropriately, focusing on the inductive / deductive process that from the starting hypotheses allows one to reach conclusions. In addition to the specific interest in understanding modern physics, the topics covered are particularly important for preparing mathematics and physics teaching job interviews.

In particular, and with reference to the so-called Dublin Descriptors, the course aims to provide the following knowledge and skills.

Knowledge and understanding abilities

Knowledge of the main phenomenological and theoretical aspects related to special relativity, statistical mechanics, quantum mechanics, with elements of nuclear physics; understanding of their physical implications and their mathematical description.

Applying knowledge and understanding ability

Ability to recognize the main laws that govern modern physics, and to apply them to solve problems and exercises at different levels of complexity and therefore of approximation, with the use of appropriate mathematical tools.

Ability of making judgements

Evaluation of the order of magnitude of the variables that describe a relativistic or quantum phenomenon. Evaluation of the relevance of a physical law (axiom, principle of conservation, universal law, theorem, law in global/integral or local/differential form and its generality, properties of materials, etc.). Ability to be able to evaluate the Physical Model and the corresponding Mathematical Model that best apply to the description of a physical process and therefore to the solution of quantitative problems.

Communication skills

Ability to present scientific concepts belonging to Physics but also, and more generally, information, ideas, problems and solutions with properties and inambiguity of language, at different levels and to different, both specialists and non-specialists, audiences.

Learning skills

Ability to learn the scientific concepts of Physics, necessary to undertake subsequent studies with a high degree of autonomy.

- Elements of the special theory of relativity.

- Introduction to statistical mechanics.

- Introduction to quantum mechanics.

Elements of special theory of relativity and elements of general relativity
Michelson-Morley experience. Operational definition of space and time measurements - Space-time interval - Temporal order and spatial separation of events - Proper time - Postulates of the theory of special relativity - Lorentz transformations - Algebraic-geometric properties of Lorentz transformations - Transformations of velocity - Transformations of momentum, energy and force - Twin paradox - Aberration and Doppler effect.

Introduction to statistical mechanics. Atomistic hypothesis of matter. Brownian motion.

Introduction to quantum mechanics. Black body radiation and Planck's hypothesis - Photoelectric effect - Compton effect - Atomic models by Thomson, Rutherford and Bohr - De Broglie relation - Diffraction of electrons - Heisenberg uncertainty principle - Wave function concept and interpretation probabilistic. Schrödinger equation - Particle in a potential well - Tunnel effect - Quantum harmonic oscillator - Atomic spectroscopic series - Hydrogen atom.

- Introduction to the structure of matter: a course in modern physics, J. J. Brehm, W. J. Mullin, Wiley, 1989

- Introduzione alla relatività ristretta, R. Resnick, CEA, 1979