Oscillator Physics

The oscillator is an essential concept in physics: matter is often modeled by a collection of oscillators (harmonic or not) interacting with each other and with the external environment. The latter acts on matter via a wave, such as an acoustic or electromagnetic wave. This lays the theoretical foundations for the problems of radiation-matter inter-action, and thus for the construction of one of the fundamental tools for the study of matter (in the broadest sense): spectroscopy.

Spectroscopy is the basic tool for studying the physical properties of the objects that surround 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 is then a means of discovering the various types of oscillators making up the medium under study.

 In short, the study of the physical environments that surround us requires the use of two fundamental theoretical tools: oscillators and waves, which are the subject of this course.  

The principle adopted here is a step-by-step progression from the harmonic oscillator, then coupled oscillators, to waves treated as discrete systems: infinite then finite coupled oscillators with different edge conditions.

Acquire the basic knowledge needed to interpret certain spectroscopy experiments. Know how to perform mode calculations and construct general solutions using modal superpositions. Basic knowledge of waves and dispersion relations.

Basic Newtonian dynamics: point mechanics: elementary oscillators.  

Mastery of basic mathematics (L1): analysis and algebra.

Recommended prerequisites* : Any in-depth knowledge of point mechanics.

100% CT

1 - Oscillators: The harmonic oscillator (definition, solution, phase space, energy). Potential method (reminder, potential, non-linear oscillations, linear limit). Forced and damped oscillator (equation of motion, solution, power consumption).

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


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