Quantum Mechanics, Volume 3. Claude Cohen-Tannoudji

      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

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