# INSTITUTIONS OF THEORETICAL PHYSICS

Academic Year 2023/2024 - Teacher: Fabio SIRINGO

## Expected Learning Outcomes

Full knowledge and understanding of  the foundations of special relativity and quantum mechanics. Ability to solve simple problems on elementary physical systems by the methods of quantum mechanic and classical electromagnetism. For more details on  the content see also the "AVVISI" tab in: www.dfa.unict.it/corsi/L-30/docenti/fabio.siringo

## Course Structure

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

## Required Prerequisites

Calculus,  General Physics

## Detailed Course Content

Classic and Relativistic Mechanics: Lagrangian and Hamiltonian formalism. Symmetries and conserved quantities, canonical transformations, generators. Lorentz transformations, covariant formalism, eq. of  motion and Maxwell eqs. in covariant form. Gauge invariance and charge conservation. Electromagnetic waves,  wave packets and the limit of geometric optics.

Foundations of Quantum Mechanics:  Feynman path integrals, derivation of  the Schr¨odinger eq. Axioms of the measurement process, linear space of physical states, linear operators, physical observables, unitary operators, Dirac formalism. Symmetries and  generators, position and momentum operators, uncertainty relations, angular momentum, time evolution and the Schr¨odinger eq., Heisenberg representation, classical limit.

Simple applications of  Quantum Mechanics: one-dimensional problems: free particle, potential well, harmonic oscillator. Tridimensional problems: features and spectrum of the angular momentum, spherical armonics, central potential, hydrogenoid atom, harmonic oscillator in three dimensions, composition of angular momentum operators, Pauli theory of spin. Interaction with an electromagnetic field: general fetures,  gauge invariance and local U(1) symmetry, Landau levels and quantum  Hall effect.

Approximate methods: Variational method, time-independent and time-dependent perturbation theory. Helium atom, Atomo di elio, hydrogenoid atom in an e.m. field., dipole transitions.

For more details see the "AVVISI" tab in:  www.dfa.unict.it/corsi/L-30/docenti/fabio.siringo

## Textbook Information

1) R. Shankar, Principles of Quantum Mechanics, Springer.

2) C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics Vol.I e II, Wiley.

3)  L.D. Landau, E.M. Lifsits, Vol.I Meccanica, Vol. II Teoria dei Campi e Vol. III Meccanica Quantistica, Editori Riuniti.

## Course Planning

SubjectsText References
1Special Relativity and Electromagnetism in the covariant formalism 1-2-3
2Foundations of  Quantum Mechanics1-2-3
3Harmonic Oscillator1-2-3
4Angular Momentum1-2-3
5Hydrogen atom1-2-3
6Composition of angular momentum operators and Pauli theory of spin1-2-3
7Approximate methods (variational method and perturbation theory) 1-2-3
8Gauge change and local U(1) invariance1-2-3

## Learning Assessment

### Learning Assessment Procedures

Written test, with exercises, and colloquium.

### Examples of frequently asked questions and / or exercises

Many exercises can be found in  the  "AVVISI" tab of  the web page:  www.dfa.unict.it/corsi/L-30/docenti/fabio.siringo