Statistical Mechanics: A Set Of Lectures
1. Introduction to Statistical Mechanic
2. Density Matrices
3. Path Integrals
4. Classical System of N Particles
5. Order-Disorder Theory
Chapter 6 Creation and Annihilation Operators
6.1 A Simple Mathematical Problem . .
6.2 The Linear Harmonic Oscillator . .
6.3 An Anharmonic Oscillator ....
6.4 Systems of Harmonic Oscillators . .
6.5 Phonons .........
6.6 Field Quantization ......
6.7 Systems of Indistinguishable Particles .
6.8 The Hamiltonian and Other Operators
6.9 Ground State for a Fermion System .
6.10 Hamiltonian for a Phonon-Electron Systerr
6,1) Photon-Electron Interactions
6.12 Feynman Diagrams . . .
Chapter 7 Spin Waves
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
Spin-Spin Interactions
The Pauli Spin Algebra
Spin Wave in a Lattice
Semiclassical Interpretation of Spin Wave
Two Spin Waves
Two Spin Waves (Rigorous Treatment)
Scattering of Two Spin Waves . . .
Non-Orthogonality ......
Operator Method
Scattering of Spin Waves-Oscillator Analog
Chapter 8 Polaron Problem
8.1
8.2
8.3
8.4
8.5
Introduction
Perturbation Treatment of the Polaron Problem
Formulation for the Variational Treatment .
The Variational Treatment
Effective Mass . . .
Contents
Chapter 9 Electron Gas in a Metal
Introduction: The State Function
Sound Waves.
Calculation of P(R)
Correlation Energy
Plasma Oscillation
Random Phase Approximation.
Variational Approach
Correlation Energy and Feynman Diagrams
Higher-Order Perturbation .....
Chapter 10 Superconductivity
10.1 Experimental Results and Early Theory ....
10.2 Setting Up the Hamiltonian .......
10.3 A Helpful Theorem ..........
10.4 Ground State of a Superconductor .....
10.5 Ground State of a Superconductor {continued) . .
IC.6 Excitations ............
10.7 Finite Temperatures. .........
10.8 Real Test of Existence of Pair States and Energy Gap
10.9 Superconductor with Current .......
10.10 Current Versus Field .........
10.11 Current at a Finite Temperature ......
10.12 Another Point of View
Chapter II Superfluidity
Introduction: Nature of Transition ......
Superfluidity n Early Approach ......
Intuitive Derivation of Wave Functions: Ground State.
Phonons and Rotons ..........
Rotons ...............
Critical Velocity
[rrotational Superfluid Flow . . .
Rotational of the Superfluid . . .
A Reasoning Leading to Vortex Lines
The X Transition in Liquid Helium ,