Statistical Mechanics for Beginners

The following sections are included:

• Preface

• Contents

• List of Figures

• Physical Constants

The following sections are included:

• The Thermodynamic Potentials
  • The entropy as a thermodynamic potential
  • The Helmholtz free energy as a potential
  • The grand potential

The following sections are included:

• The Microcanonical Ensemble

• Properties of the Entropy

• An Example

The following sections are included:

• The Canonical Ensemble
  • The partition function
  • Energy, entropy and thermodynamic potential
  • A two-level system
  • The ideal gas; equipartition of energy in classical mechanics

• The Grand Canonical Ensemble
  • The grand partition function
  • The number of particles, energy, entropy and the grand potential
  • An example

• Summary
  • Fluctuations
  • Final remark

The following sections are included:

• The Partition Function and the Free Energy
  • For variable N and for fermions
  • For variable N and for bosons
  • For fixed N, and for both fermions and bosons

• The Energy and the Entropy

• The Classical Ideal Gas: Maxwell–Boltzmann Statistics

• Qualitative Behavior of the Chemical Potential and the Derivation of (∂μ/∂T)V,N < 0
  • Bosons
  • Fermions

The following sections are included:

• The Wave Vector

• The Density of States

• The Monatomic Ideal Gas
  • The partition function
  • The internal energy, entropy and equation of state
  • The classical limit

The following sections are included:

• The Quantum Harmonic Oscillator
  • Low temperature limit
  • High temperature limit

• The Polyatomic Ideal Gas

• Bosons and Fermions in a Two-Level System
  • The particles are bosons
  • The particles are fermions
  • Classical particles

• The Magnetic Chain

In the first part, we developed the basic principles of statistical mechanics. Now we use them to study some real situations. They are physical problems which were studied experimentally and received complete explanation by the methods developed in the first part…

The following sections are included:

• The Energy and the Energy Spectrum

• The Free Energy and the Entropy
  • The relation with the wave picture

• Light Emission and Absorption of Solids; Kirchhoff's Law

• The Black Body Emission

• The Properties of Photon Gas are Independent of the Shape and the Material of the Cavity

The following sections are included:

• Atomic Vibration in Solids

• The Properties of Phonons

• The Low Temperature Case

• The High Temperature Case

• The Debye Formula

• Resolution of the Differential Equation (7.1) by Means of Trigonometric Functions

• Derivation of the Expression (7.30) Giving C_V in the Debye Model

The following sections are included:

• The Chemical Potential

• The Energy, Specific Heat, Free Energy and Entropy

• Experimental Verification

The following sections are included:

• Free Electrons in a Box
  • The Fermi–Dirac function
  • The chemical potential or the Fermi level
  • The energy
  • The specifc heat
  • Applications to metals

• Electrons in Semiconductors

The following sections are included:

• Thermodynamics and Statistical Mechanics Before Maxwell and Bolztmann

• The Kinetic Theory of Maxwell

• Boltzmann and Irreversibility

• Gibbs, the Father of Statistical Mechanics

• Planck and Einstein: Quantum Theory and Statistics

• The Method of Bose and the Bose–Einstein Condensation

• The Principle of Pauli and the Statistics of Fermi and Dirac

• Modern Developments

The following sections are included:

• Exercises

• Index