Quantum physics - 4PMGPHQ1

Part 1: Stationary quantum physics
======================================================
Chapter 1 - Bound states in a central field
Commutation with angular momentum
Spherical harmonics
Radial Schrödinger equation

Chapter 2 - Spectrum of the hydrogen atom
Electrons bound by coulomb force
Energies and wavefunctions of the hydrogen atom

Chapter 3 - Stationnary perturbation theory
Perturbation method
First and second order perturbation of a nondegenerate state
Case of degenerate states
Application to relativistic corrections of the hydrogen atom

Chapter 4 - Addition of angular momentum
Case of two spin 1/2
Basics of tensor product
General addition theorem

Chapter 5 - Fine and hyperfine structure of the hydrogen atom
Electron spin angular momentum
Spin-orbit coupling and fine structure
Spin-spin coupling and hyperfine structure
The modern definition of the second

Chapter 6 - Identical particles
Indistinguishable identical particles
Fermions and bosons, Pauli exclusion principle, connection between spin and statistics
Physical consequences, stability of neutrons in nuclei

Part 2 : Interrogating quantum systems
================================================
Chapter 7 Magnetic resonance
Dynamics of a spin 1/2 in a magnetic field
Larmor precession
Rabi resonance
Time-energy uncertainty

Chapter 8 Quantum dynamics
Time dependent perturbation theory at first order
Fermi golden rule
Scattering theory, Born approximation

Problems
========
Quantum harmonic oscillator 1D and 3D
Bound states in a 3D square potential
Wan der Waals force
Influence of a magnetic field on the hyperfine structure
Ramsey resonance
Harmonic perturbation of a two states system
Scattering by Yukawa potential, Rutherford scattering

Written exam (2h)

Jean-Louis Basdevant, Jean Dalibard, Mécanique quantique, Les Éditions de l'École Polytechnique