Quantum Mechanics

Claude Cohen-Tannoudji was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris where he also studied and received his PhD in 1962. In 1973 he became Professor of atomic and molecular physics at the Collège des France. His main research interests were optical pumping, quantum optics and atom-photon interactions. In 1997, Claude Cohen-Tannoudji, together with Steven Chu and William D. Phillips, was awarded the Nobel Prize in Physics for his research on laser cooling and trapping of neutral atoms. Bernard Diu was Professor at the Denis Diderot University (Paris VII). He was engaged in research at the Laboratory of Theoretical Physics and High Energy where his focus was on strong interactions physics and statistical mechanics. Franck Laloë was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris. His first assignment was with the University of Paris VI before he was appointed to the CNRS, the French National Research Center. His research was focused on optical pumping, statistical mechanics of quantum gases, musical acoustics and the foundations of quantum mechanics.

WAVES AND PARTICLES: INTRODUCTION TO THE FUNDAMENTAL CONCEPTS OF QUANTUM MECHANICS
Electromagnetic Waves and Photons
Material Particles and Matter Waves
Quantum Description of a Particle; Wave Packets
Particle in a Time-Independent Scalar Potential
Complements

THE MATHEMATICAL TOOLS OF QUANTUM MECHANICS
One-Particle Wave Function Space
State Space. Dirac Notation
Representations in the State Space
Eigenvalue Equations. Observables
Two Important Examples of Representations and Observables
Tensor Product of State Spaces
Complements

THE POSTULATES OF QUANTUM MECHANICS
Introduction
Statement of the Postulates
The Physical Interpretation of the Postulates
The Physical Implications of the Schrödinger Equation
The Superposition Principle and Physical Predictions
Complements

APPLICATION OF THE POSTULATES TO SIMPLE CASES: TWO LEVEL SYSTEMS AND SPIN 1/2 SYSTEMS
Spin 1/2 Particle: Quantization of the Angular Momentum
Illustration of the Postulates in the Case of a Spin 1/2
General Study of Two-Level Systems
Complements

THE ONE DIMENSIONAL HARMONIC OSCILLATOR
Introduction
Eigenvalues of the Hamiltonian
Eigenstates of the Hamiltonian
Complements

GENERAL PROPERTIES OF ANGULAR MOMENTUM IN QUANTUM MECHANICS
Introduction: The Importance of Angular Momentum
Commutation Relations Characteristic of Angular Momentum
General Theory of Angular Momentum
Application to Orbital Angular Momentum
Complements

PARTICLES IN A CENTRAL POTENTIAL. THE HYDROGEN ATOM
Stationary States of a Particle in a Central Potential
Motion of the Center of Mass and Relative Motion for a System of Two Interacting Particles
The Hydrogen Atom
Complements