# Quantum Mechanics

## Volume III: Fermions, Bosons, Photons, Correlations, and Entanglement

1. Edition October 2019

784 Pages, Hardcover

150 Pictures*Textbook*

**978-3-527-34555-7**

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This new, third volume of Cohen-Tannoudji's groundbreaking textbook covers advanced topics of quantum mechanics such as uncorrelated and correlated identical particles, the quantum theory of the electromagnetic field, absorption, emission and scattering of photons by atoms, and quantum entanglement. Written in a didactically unrivalled manner, the textbook explains the fundamental concepts in seven chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications.

* Completing the success story: the third and final volume of the quantum mechanics textbook written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard Diu and Franck Laloë

* As easily comprehensible as possible: all steps of the physical background and its mathematical representation are spelled out explicitly

* Comprehensive: in addition to the fundamentals themselves, the books comes with a wealth of elaborately explained examples and applications

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.

General Formalism

One-Particle Symmetric Operators

Two-Particle Operators

Complements

FIELD OPERATOR

Definition of the Field Operator

Symmetric Operators

Time Evolution of the Field Operator (Heisenberg Point of View)

Relation to Field Quantization

Complements

PAIRED STATES OF IDENTICAL PARTICLES

Creation and Annihilation Operators of a Pair of Particles

Building Paired States

Properties of the Kets Characterizing the Paired States

Correlations Between Particles, Pair Wave Function

Paired States as a Quasi-Particle Vacuum; Bogolubov-Valatin Transformations

REVIEW OF CLASSICAL ELECTRODYNAMICS

Classical Electrodynamics

Describing the Transverse Field as an Ensemble of Harmonic Oscillators

Complements

QUANTIZATION OF ELECTROMAGNETIC RADIATION

Quantization of the Radiation in the Coulomb Gauge

Photons, Elementary Excitations of the Free Quantum ¿eld

Description of the Interactions

Complements

ABSORPTION, EMISSION AND SCATTERING OF PHOTONS BY ATOMS

A Basic Tool: the Evolution Operator

Photon Absorption Between Two Discrete Atomic Levels

Stimulated and Spontaneous Emissions

Role of Correlation Functions in One-Photon Processes

Photon Scattering by an Atom

Complements

QUANTUM ENTANGLEMENT, MEASUREMENTS, BELL'S INEQUALITIES

Introducing Entanglement, Goals of This Chapter

Entangled States of Two Spin-1/2 Systems

Entanglement Between More General Systems

Ideal Measurement and Entangled States

"Which Path" Experiment: Can One Determine the Path Followed by the Photon in Young's Double Slit

Entanglement, Non-Locality, Bell's Theorem

Complements

APPENDIX: FEYNMAN PATH INTEGRAL

Quantum Propagator of a Particle

Interpretation in Terms of Classical Histories

Discussion. A New Quantization Rule

Operators

APPENDIX: LAGRANGE MULTIPLIERS

Function of Two Variables

Function of N Variables

APPENDIX: BRIEF REVIEW OF QUANTUM STATISTICAL MECHANICS

Statistical Ensembles

Intensive or Extensive Physical Quantities

APPENDIX: WIGNER TRANSFORM

Delta Function of an Operator

Wigner Distribution of the Density Operator (Spinless Particle)

Wigner Transform of an Operator

Generalizations

Discussion: Wigner Distribution and Quantum Effects

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.