Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 2

1  Cover

2  Foreword

3  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 A_XV 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 B_XV 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 C_XV Condensed boson system, Gross-Pitaevskii equation 1. Notation, variational ket 2. First approach 3. Generalization, Dirac notation 4. Physical discussion Complement D_XV Time-dependent Gross-Pitaevskii equation 1. Time evolution 2. Hydrodynamic analogy 3. Metastable currents, superfluidity Complement E_XV Fermion system, Hartree-Fock approximation 1. Foundation of the method 2. Generalization: operator method Complement F_XV Fermions, time-dependent Hartree-Fock approximation 1. Variational ket and notation 2. Variational method 3. Computing the optimizer 4. Equations of motion Complement G_XV Fermions or Bosons: Mean field thermal equilibrium 1. Variational principle 2. Approximation for the equilibrium density operator 3. Temperature dependent mean field equations Complement H_XV 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

4  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 A_XVI 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 B_XVI Spatio-temporal correlation functions, Green’s functions 1. Green’s functions in ordinary space 2. Fourier transforms 3. Spectral function, sum rule Complement C_XVI Wick’s theorem 1. Demonstration of the theorem 2. Applications: correlation functions for an ideal gas

5  Chapter: XVII Paired states particles of identical 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 A_XVII 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 B_XVII 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 C_XVII Fermion pairing, BCS theory 1. Optimization of the energy 2. Distribution functions, correlations 3. Physical discussion 4. Excited states Complement D_XVII 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 E_XVII Condensed repulsive bosons 1. Variational state, energy 2. Optimization 3. Properties of the ground state 4. Bogolubov operator method

6  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 A_XVIII 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

7  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 A_XIX 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 B_XIX 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 variables2047 3. Discussion Complement C_XIX 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

8  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 A_XX A multiphoton process: two-photon absorption 1. Monochromatic radiation 2. Non-monochromatic radiation 3. Discussion Complement B_XX 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 C_XX 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 Complement D_XX Light shifts: a tool for manipulating atoms and fields 1. Dipole forces and laser trapping 2. Mirrors for atoms 3. Optical lattices 4. Sub-Doppler cooling. Sisyphus effect 5. Non-destructive detection of a photon Complement E_XX Detection of one- or two-photon wave packets, interference 1. One-photon wave packet, photodetection probability 2. One- or two-photon interference signals 3. Absorption amplitude of a photon by an atom 4. Scattering of a wave packet 5. Example of wave packets with two entangled photons

9  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 COMPLEMENTS OF CHAPTER XXI, READER’S GUIDE Complement A_XXI Density operator and correlations; separability 1. Von Neumann statistical entropy 2. Differences between classical and quantum correlations 3. Separability Complement B_XXI GHZ states, entanglement swapping 1. Sign contradiction in a GHZ state 2. Entanglement swapping Complement C_XXI Measurement induced relative phase between two condensates 1. Probabilities of single, double, etc. position measurements 2. Measurement induced enhancement of entanglement 3. Detection of a large number Q of particles Complement D_XXI Emergence of a relative phase with spin condensates; macroscopic non-locality and the EPR argument 1. Two condensates with spins 2. Probabilities of the different measurement results 3. Discussion

10  Appendix IV: Feynman path integral 1. Quantum propagator of a particle 2. Interpretation in terms of classical histories 3. Discussion; a new quantization rule 4. Operators

11  Appendix V: Lagrange multipliers 1. Function of two variables 2. Function of AT variables

12  Appendix VI: Brief review of Quantum Statistical Mechanics 1. Statistical ensembles 2. Intensive or extensive physical quantities

13  Appendix VII: Wigner transform 1. Delta function of an operator 2. Wigner distribution of the density operator (spinless particle) 3. Wigner transform of an operator 4. Generalizations 5. Discussion: Wigner distribution and quantum effects

14  Bibliography of volume III

15  Index

16  End User License Agreement