Physics of Oscillators

The oscillator is a fundamental concept in physics: matter is often modeled as a collection of oscillators (harmonic or otherwise) that interact with one another and with the external environment. The environment acts on the matter through a wave, such as an acoustic or electromagnetic wave. This allows us to lay the theoretical foundations for problems involving radiation-matter interaction and thus to develop one of the fundamental tools for the study of matter (in the broadest sense): spectroscopy.

Spectroscopy is, in fact, the fundamental tool for studying the physical properties of the objects around us, such as molecules, crystals, stars, and galaxies. These properties are deduced either from their spontaneous emission or from their response to external excitation. For example, we measure the absorption, reflection, and transmission properties of applied electromagnetic radiation (visible, infrared, X-rays, neutrons, etc.). The response to this radiation then provides a way to identify the various types of oscillators that make up the medium under study.

 In short, the study of the physical environments around us relies on two fundamental theoretical tools: oscillators and waves, which are precisely the subject of this course.  

The approach taken here is a step-by-step progression, starting with the harmonic oscillator, then moving on to coupled oscillators, and finally to waves analyzed within the framework of discrete systems: infinite and then finite coupled oscillators with different boundary conditions.

Acquire the basic knowledge necessary to interpret certain spectroscopy experiments. Be able to perform mode calculations and construct general solutions using modal superposition. Basic knowledge of waves and dispersion relations.

Basic Newtonian Dynamics: Point Mechanics: Elementary Oscillators.  

Bachelor's Degree in Basic Mathematics (L1): Analysis and Algebra.

Recommended prerequisites*: A thorough understanding of point mechanics.

CT 100%

1 - Oscillators: 
Theharmonic oscillator(definition, solution, phase space, energy).
The potential method(review, potential, nonlinear oscillations, linear limit).
Forced and damped oscillators(equation of motion, solution, absorbed power)
.

2 - Coupled oscillators: 
Twooscillators(equations, natural frequencies, eigenmodes).
Coupled particles(diatomic molecule, eigenmodes of CO2).


3 - Waves in Molecular Chains: Coupled-particle system(potential energy, equations of motion, modes, dispersion relation, transverse and longitudinal traveling waves, band-edge waves, evanescent waves). 
Finite system of coupled particles(boundary conditions, standing waves, fixed, free, and periodic ends). 
Forced end(monochromatic forcing, signal propagation, low-pass filter, resonant forcing , transmitted power, attenuation). Diatomic chain(dispersion relation, gap opening, acoustic branch, and optical branch). Chain of coupled oscillators, band gap(dispersion relation, traveling and standing waves, evanescent wave, wave packet, phase and group velocities, bandwidth, Schrödinger equation, wave packet broadening).