Lýsing:
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.
Annað
- Höfundar: Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë
- Útgáfa:1
- Útgáfudagur: 2020-06-05
- Hægt að prenta út 10 bls.
- Hægt að afrita 2 bls.
- Format:ePub
- ISBN 13: 9783527822751
- Print ISBN: 9783527345557
- ISBN 10: 3527822755
Efnisyfirlit
- Cover
- Foreword
- 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
- 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
- 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
- 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
- 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 variables2047
- 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
- 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
- Complement DXX 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 EXX 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
- 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 AXXI Density operator and correlations; separability
- 1. Von Neumann statistical entropy
- 2. Differences between classical and quantum correlations
- 3. Separability
- Complement BXXI GHZ states, entanglement swapping
- 1. Sign contradiction in a GHZ state
- 2. Entanglement swapping
- Complement CXXI 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 DXXI 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
- 1. Quantum propagator of a particle
- 2. Interpretation in terms of classical histories
- 3. Discussion; a new quantization rule
- 4. Operators
- 1. Function of two variables
- 2. Function of AT variables
- 1. Statistical ensembles
- 2. Intensive or extensive physical quantities
- 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
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- Höfundur : 15579
- Útgáfuár : 2020
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