Contents page PARTI SECOND QUANTIZATION 1 Elementary quantum mechanics 1.1 Classical mechanics 3 2 Schrodinge Dirac formulation Schrodinger and Heisenberg pictures 1.5 Perturbation theory 1.6 Time-dependent perturbation theory 1 1.6.1 Fermi's golden rule 8 1.7 and momentum 1.7.2 045 Iwo spins 1.8 Two-level system:The qubit 6 1.9 Harmonic oscillator 2 1.10 The density matrix 31 Exercises 38 Solutions 41 2 ldentical partides 43 2.1 Schrodinger equation for identical particles 4 2.2 The symme etry postulate 47 Quantum fields 2.3 Solutions of the N-particle Schrodinger equation 80 2.3.1 Symmetric wave function:Bosons 5 232 Antisymmetric wave function:Fermions 233 Fock space 56 Exercises Solutions 96 3 Second quantization 6 3.1 Second quantization for bosons 3.1.1 Commutation relations 3.1.2 The cture of Fock space Contents Figure Credits page x Preface xi PART I SECOND QUANTIZATION 1 1 Elementary quantum mechanics 3 1.1 Classical mechanics 3 1.2 Schrödinger equation 4 1.3 Dirac formulation 7 1.4 Schrödinger and Heisenberg pictures 11 1.5 Perturbation theory 13 1.6 Time-dependent perturbation theory 14 1.6.1 Fermi’s golden rule 18 1.7 Spin and angular momentum 20 1.7.1 Spin in a magnetic field 24 1.7.2 Two spins 25 1.8 Two-level system: The qubit 26 1.9 Harmonic oscillator 29 1.10 The density matrix 31 1.11 Entanglement 33 Exercises 38 Solutions 41 2 Identical particles 43 2.1 Schrödinger equation for identical particles 43 2.2 The symmetry postulate 47 2.2.1 Quantum fields 48 2.3 Solutions of the N-particle Schrödinger equation 50 2.3.1 Symmetric wave function: Bosons 52 2.3.2 Antisymmetric wave function: Fermions 54 2.3.3 Fock space 56 Exercises 59 Solutions 61 3 Second quantization 63 3.1 Second quantization for bosons 63 3.1.1 Commutation relations 64 3.1.2 The structure of Fock space 65 v