2019: Quantum Mechanics I and General Relativity

At the moment I am teaching two courses, Quantum Mechanics I in spring and General Relativity in autumn. The course material is also available on moodle if you are one of our students.

• Quantum Mechanics I (pdf, 2.6MB): A first (theoretical) quantum mechanics course at bachelor level. The course starts with the wave function and simple 1D examples. It then introduces the standard bra-ket formalism and discusses the harmonic oscillator, the classical limit and the uncertainty relation. It then solves the hydrogen atom, and discusses angular momentum and spin. It ends with entanglement, the EPR paradox and a few simple quantum information examples.
• General Relativity (pdf, 2.5MB): An introductory GR course at master level. The first chapter introduces the mathematical formalism and then ``derives'' the Einstein field equations. It also presents the Lagrangian formalism and a brief discussion of the Lovelock theorem. The second chapter deals with linearized gravity and nearly Newtonian fields, graviational waves and gravitational lensing. The third chapter derives the Schwarzschild solution and its geodesics, and discusses the classical tests of GR. The last part is dedicated to black holes.

Winter 2015: Deux cours pour Physique d'Aujourd'hui

I am giving again two classes of the "Physique d'Aujourd'hui" lecture series. These are public lectures that also serve as an introduction to contemporary research for the first year physics students. The 2014 slides (in French) for my two classes can be found here:

• Peser l'Univers avec l'écho du big bang et des étoiles explosives (pdf, 13MB)
• De l'infiniment grand à l'infiniment petit: l'Univers comme laboratoire pour la physique fondamentale (pdf, 10MB)

Winter 2015: Thermodynamics, elasticity and fluid dynamics

My previous main course was about classical thermodynamics, elasticity and fluid dynamics. There are all effective theories that describe the behaviour of continuous media. You can download my 2015 lecture notes here (pdf, 4MB). You can also get the course material on chamilo during term if you are one of our students.

Winter 2010 / Summer 2011: Méthodes Mathématiques pour Physiciens

Until the academic year 2010/11 I have been teaching several times the lecture 12P015, méthodes mathématiques pour physiciens II. This is a required course for second-year students in the bachelor program. It takes place both winter and summer semester on wednesdays from 1.15pm until roughly 4pm in the auditoire Stückelberg. The course consists of a short theoretical introduction followed by exercises. In addition to me there are usually two assistants present; I am very grateful for their help throughout the year -- the course would not be have been possible without them.

syllabus

This course aims at building up some of the mathematical background required for the other physics subjects. It puts a heavy emphasis on solving exercises. You can download the 2010/11 version of the lectures notes (pdf, 911kB) (in French). It contains the following chapters:

1. Les distributions et la fonction delta de Dirac
2. Fonctions de Green
3. Tenseurs
4. Probabilités et Statistique
5. Intégration complexe
6. Groupes
7. Espaces de Hilbert

Most of the lecture notes were originally created by Werner Amrein (distributions, Greens functions, tensors, Hilbert spaces), Jean-Pierre Imhof (probability and statistics) and Henri Ruegg (group theory). The notes were then modified and extended by other lecturers, notably Michel Droz, Cathérine Leluc and Xin Wu (probability and statistics), Eugène Sukhorukov (distributions, Greens functions), Olivier Piguet and Michele Maggiore (group theory), and Ruth Durrer (Hilbert spaces, Greens functions). Mathias Albert helped a lot with the complex integration chapter, and Umberto Cannella provided decisive support when we unified all the notes a few years ago. The lecture is now (academic year 2011/12) given by Vincent Desjacques.

Summer 2005: Cosmology II

I'm teaching cosmology II this summer term (2005), every thursday morning from 10:15 to 12:00 in room 222 of Sciences-I. The exercises classes are given by Marcus Ruser and take place every other week on thursdays at 8:15. This is a course in theoretical physics which emphasises the mathematical methods used in understanding the evolution of the universe (i.e. better don't expect many pretty pictures).

syllabus

The lecture is roughly split into two halves. The first one discusses the homogeneous (Friedmann-Lemaitre-Robertson-Walker) universe and its thermal history. The second part discusses shortcomings of this model, how inflation can solve them and generate perturbations. We then compute the evolution of those perturbations.

1. The homogeneous universe
• The geometrical structure of the universe
• The dynamics of the universe
• Thermal history of the universe
2. The perturbed universe
• Problems of the standard model
• The inflationary universe
• Evolution of perturbations and formation of structure
• The cosmic microwave background

literature

There are many excellent introductory and advanced texts on cosmology, and it is impossible to mention them all. Here I only list those that were used most in the preparation of the lecture notes.

• Ruth Durrers lecture notes (in French). I like especially the very rigorous treatment of the FRW geometry.
• Scott Dodelson, Modern Cosmology: An modern and very pedagogical book, highly recommended.
• Edward Kolb and Michael Turner, The Early Universe: One of the standard textbooks. It contains a wealth of information, but it is not always easy to avoid getting lost. My thermal history chapter follows quite closely the treatment in this book.
• Andrew Liddle and David Lyth, Cosmological Inflation and Large Scale Structure: A good standard textbook on inflation, and the basis of my chapter on inflation.
• T. Padmanabhan, Structure formation in the universe: A good introduction into the evolution of cosmological perturbations and the formation of structure.

lecture notes

The lecture notes are available as a gzipped PS file (1.9MB) or as a pdf file (1MB). The notes are still (and probably will forever be) in a preliminary state. I am grateful for any feedback, especially if you found some mistakes!

exercises (by Marcus Ruser)

There are four series available as pdf files, covering:

1. The FLRW metric and the Friedmann equations
2. Thermal history I
3. Thermal history II
4. Inflation and tensor perturbations