Degrees incorporating this pedagocial element :

### Description

This course is in two parts: the first is a more in-depth exploration of the quantum mechanics concepts presented in the Physics bachelor, in particular introducing the different resolution methods. The second focuses on a detailed description of atoms.

Quantum Mechanics part

- **Chapter I: Introduction, reviews: **assumptions, wave function and Dirac notation, operators and measurement theory, Schrödinger equation, Heisenberg uncertainty principle

- **Chapter II: Harmonic potential: **harmonic oscillator (review), Schrödinger equation in the presence of a magnetic field (gauge invariance), electromagnetic field quantification

- **Chapter III: ** **Angular momentum:** spin ½, spin Hamiltonian (precession), fermions/bosons, momentum coupling (degrees of freedom, tensor product of Hilbert spaces, Clebsch-Gordan coefficients)

- **Chapter IV: ** **Symmetries and conservation laws**: symmetry groups (Noether's theorem), generators and degeneracy, periodic potential (Bloch), Runge-Lenz invariance in central potentials

- **Chapter V: Approximation methods: **stationary (first and second order, degenerate states) and time-dependent perturbations (Fermi's golden rule, Wigner-Eckhart theorem), variational method, Wayl and Sommerfeld formulae

- **Chapter VI: Scattering theory **(part I): introduction, scattering amplitude, Born approximation

Atomic Physics part

- **Chapter VII: Hydrogen atom: **review, fine and hyperfine structures, atom-photon interaction (classical/quantum)**, **density operator, Bloch equation, systems involving several electrons (helium, Hund's rules)

** - Chapter VIII:** **Cold atoms:** scattering (part II), modern experiments in atomic physics, Bell's inequalities

### Prerequisites

Quantum Mechanics bachelor (L3) course (formalism, wave-particle duality, black-body and photons, Heisenberg uncertainty principle, Schrödinger equation, potential wells and barriers, harmonic oscillator, hydrogen atom and spin ½).

### Bibliography

Mécanique quantique (volumes 1 et 2) par Claude Cohen-Tannoudji ou tout autre ouvrage de mécanique quantique

Introduction to quantum optics par G. Grynberg, A. Aspect et C. Fabre.