# Oscillations and Waves

**Academic Year 2022/2023**- Teacher:

**Giovanni PICCITTO**

## Expected Learning Outcomes

At the end of the course students are requested to be able to recognize and understand the characteristics of oscillating and wave phenomena and to describe them mathematically as aprelude of the quantum mechanics.

## Course Structure

Lectures and practical numerical exercise in Matlab.

Should the circumstances require online or blended teaching, appropriare modification to what is hereby stated may be introduced, in order to achieve the mai objectives of the course.

## Required Prerequisites

Fisica I, Analisi Matematica I## Detailed Course Content

Harmonic function. Fourier series and transforms. Examples of harmonic oscillators. Linearity and superposition principle. Lagrangian and Hamiltonian formulations. Classical models of oscillating atomic, molecular and plasma dipoles. Damped harmonic oscillators. Q factor. Emission of classical dipoles. Forced harmonic oscillator. Impedence. Absorbed power and resonance curve. Classical model of interaction atoms-light. Oscillations of systems with N (finite) degrees of freedom. Normal modes of oscillation. Vector space. Oscillations of systems with an infinite number of degrees of freedom. Dispersion relation. Wavw equation in one dimension. D’Alembert equation. Stationary and progressive waves. Impedence and Energy flux. Analogies with a free quantum particles and a one dimensional potential well. Wave packets and group velocity. Dispersive systems. Reflection and transmission. Waves in non homogeneous systems. Impedence matching. Transmission and scattering matrix.

## Textbook Information

1) W.F. Smith,”Waves and Oscillations – A prelude to quantum mechanics”, Oxford University Press 2) H.. Georgy, “The Physics of Waves”, Prentice Hall 3) P. Markos, C.M. Soukoulis, “Wave propagation”, Princeton University Press

## Course Planning

Subjects | Text References | |

1 | Oscillatore armonico, smorzato forzato | Ref. n. 1 |

2 | Oscillatori non lineari, sistemi dinamici, spazi delle fasi | Ref. n. 1 |

3 | Sistemi finiti di oscillatori armonici accoppiati | Ref. n. 1 |

4 | Sistemi infiniti di oscillatori armonici accoppiati | Ref. n. 1 |

5 | Modello di Lorentz di interazione luce-atomo | Ref. n. 1 |

6 | Equazione d'onda e soluzioni | Ref. n. 1 |

7 | Riflessione trasmissione | Ref. n. 1 |

8 | Serie e trasformate di Fourier, delta di Dirac | Ref. n. 1 |

## Learning Assessment Procedures

Oral examination, more or less 45 min duration## Examples of frequently asked questions and / or exercises

Examples of questions:

Resonance

Wave equation

Normal modes of oscillation