Quantum Mechanics Volume 3 Fermions Bosons Photons Correlations and Entanglement 1st Edition by Claude Cohen Tannoudji, Bernard Diu, Franck Laloë 3527345558 9783527345557

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ISBN 10: 3527345558

ISBN 13: 9783527345557

Author: Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë

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 Laloe
* 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 Superieure in Paris where he also studied and received his PhD in 1962. In 1973 he became Professor of atomic and molecular physics at the College 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 Laloe was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Superieure 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.

Quantum Mechanics Volume 3 Fermions Bosons Photons Correlations and Entanglement 1st Table of contents:

Chapter XV: Creation and Annihilation Operators for Identical Particles
A. General Formalism
B. One-Particle Symmetric Operators
C. Two-Particle Operators

COMPLEMENTS OF CHAPTER XV, READER’S GUIDE
Complement AXV Particles and Holes

1. Ground State of a Non-Interacting Fermion Gas

2. New Definition for the Creation and Annihilation Operators

3. Vacuum Excitations

Complement BXV Ideal Gas in Thermal Equilibrium; Quantum Distribution Functions

1. Grand Canonical Description of a System Without Interactions

2. Average Values of Symmetric One-Particle Operators

3. Two-Particle Operators

4. Total Number of Particles

5. Equation of State, Pressure

Complement CXV Condensed Boson System, Gross-Pitaevskii Equation

1. Notation, Variational Ket

2. First Approach

3. Generalization, Dirac Notation

4. Physical Discussion

Complement DXV Time-Dependent Gross-Pitaevskii Equation

1. Time Evolution

2. Hydrodynamic Analogy

3. Metastable Currents, Superfluidity

Complement EXV Fermion System, Hartree-Fock Approximation

1. Foundation of the Method

2. Generalization: Operator Method

Complement FXV Fermions, Time-Dependent Hartree-Fock Approximation

1. Variational Ket and Notation

2. Variational Method

3. Computing the Optimizer

4. Equations of Motion

Complement GXV Fermions or Bosons: Mean Field Thermal Equilibrium

1. Variational Principle

2. Approximation for the Equilibrium Density Operator

3. Temperature Dependent Mean Field Equations

Complement HXV Applications of the Mean Field Method for Non-Zero Temperature (Fermions and Bosons)

1. Hartree-Fock for Non-Zero Temperature, A Brief Review

2. Homogeneous System

3. Spontaneous Magnetism of Repulsive Fermions

4. Bosons: Equation of State, Attractive Instability

Chapter XVI: Field Operator
A. Definition of the Field Operator
B. Symmetric Operators
C. Time Evolution of the Field Operator (Heisenberg Picture)
D. Relation to Field Quantization

COMPLEMENTS OF CHAPTER XVI, READER’S GUIDE
Complement AXVI Spatial Correlations in an Ideal Gas of Bosons or Fermions

1. System in a Fock State

2. Fermions in the Ground State

3. Bosons in a Fock State

Complement BXVI Spatio-Temporal Correlation Functions, Green’s Functions

1. Green’s Functions in Ordinary Space

2. Fourier Transforms

3. Spectral Function, Sum Rule

Complement CXVI Wick’s Theorem

1. Demonstration of the Theorem

2. Applications: Correlation Functions for an Ideal Gas

Chapter XVII: Paired States of Identical Particles
A. Creation and Annihilation Operators of a Pair of Particles
B. Building Paired States
C. Properties of the Kets Characterizing the Paired States
D. Correlations Between Particles, Pair Wave Function
E. Paired States as a Quasi-Particle Vacuum; Bogolubov-Valatin Transformations

COMPLEMENTS OF CHAPTER XVII, READER’S GUIDE
Complement AXVII Pair Field Operator for Identical Particles

1. Pair Creation and Annihilation Operators

2. Average Values in a Paired State

3. Commutation Relations of Field Operators

Complement BXVII Average Energy in a Paired State

1. Using States That Are Not Eigenstates of the Total Particle Number

2. Hamiltonian

3. Spin 1/2 Fermions in a Singlet State

4. Spinless Bosons

Complement CXVII Fermion Pairing, BCS Theory

1. Optimization of the Energy

2. Distribution Functions, Correlations

3. Physical Discussion

4. Excited States

Complement DXVII Cooper Pairs

1. Cooper Model

2. State Vector and Hamiltonian

3. Solution of the Eigenvalue Equation

4. Calculation of the Binding Energy for a Simple Case

Complement EXVII Condensed Repulsive Bosons

1. Variational State, Energy

2. Optimization

3. Properties of the Ground State

4. Bogolubov Operator Method

Chapter XVIII: Review of Classical Electrodynamics
A. Classical Electrodynamics
B. Describing the Transverse Field as an Ensemble of Harmonic Oscillators

COMPLEMENTS OF CHAPTER XVIII, READER’S GUIDE
Complement AXVIII Lagrangian Formulation of Electrodynamics

1. Lagrangian with Several Types of Variables

2. Application to the Free Radiation Field

3. Lagrangian of the Global System Field + Interacting Particles

Chapter XIX: Quantization of Electromagnetic Radiation
A. Quantization of the Radiation in the Coulomb Gauge
B. Photons, Elementary Excitations of the Free Quantum Field
C. Description of the Interactions

COMPLEMENTS OF CHAPTER XIX, READER’S GUIDE
Complement AXIX Momentum Exchange Between Atoms and Photons

1. Recoil of a Free Atom Absorbing or Emitting a Photon

2. Applications of the Radiation Pressure Force: Slowing and Cooling Atoms

3. Blocking Recoil Through Spatial Confinement

4. Recoil Suppression in Certain Multi-Photon Processes

Complement BXIX Angular Momentum of Radiation

1. Quantum Average Value of Angular Momentum for a Spin 1 Particle

2. Angular Momentum of Free Classical Radiation as a Function of Normal Variables

3. Discussion

Complement CXIX Angular Momentum Exchange Between Atoms and Photons

1. Transferring Spin Angular Momentum to Internal Atomic Variables

2. Optical Methods

3. Transferring Orbital Angular Momentum to External Atomic Variables

Chapter XX: Absorption, Emission, and Scattering of Photons by Atoms
A. A Basic Tool: The Evolution Operator
B. Photon Absorption Between Two Discrete Atomic Levels
C. Stimulated and Spontaneous Emissions
D. Role of Correlation Functions in One-Photon Processes
E. Photon Scattering by an Atom

COMPLEMENTS OF CHAPTER XX, READER’S GUIDE
Complement AXX A Multiphoton Process: Two-Photon Absorption

1. Monochromatic Radiation

2. Non-Monochromatic Radiation

3. Discussion

Complement BXX Photoionization

1. Brief Review of the Photoelectric Effect

2. Computation of Photoionization Rates

3. Is a Quantum Treatment of Radiation Necessary to Describe Photoionization?

4. Two-Photon Photoionization

5. Tunnel Ionization by Intense Laser Fields

Complement CXX Two-Level Atom in a Monochromatic Field: Dressed-Atom Method

1. Brief Description of the Dressed-Atom Method

2. Weak Coupling Domain

3. Strong Coupling Domain

4. Modifications of the Field: Dispersion and Absorption

Chapter XXI: Quantum Entanglement, Measurements, Bell’s Inequalities
A. Introducing Entanglement, Goals of This Chapter
B. Entangled States of Two Spin-1/2 Systems
C. Entanglement Between More General Systems
D. Ideal Measurement and Entangled States
E. “Which Path” Experiment: Can One Determine the Path Followed by the Photon in Young’s Double Slit Experiment?
F. Entanglement, Non-Locality, Bell’s Theorem

Appendices
Appendix IV: Feynman Path Integral
Appendix V: Lagrange Multipliers
Appendix VI: Brief Review of Quantum Statistical Mechanics
Appendix VII: Wigner Transform

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