### Table of Contents

1 Introduction

Part I QUANTUM DESCRIPTION OF SYSTEMS

2 Introduction and Basic Concepts

2.1 Systems of Identical Particles

2.2 Quantum Description of Particles

2.3 Problems with Solutions

3 Kinetic energy of Translational Motion

3.1 Hamiltonian of Translational Motion

3.2 SchrÃ¶dinger Equation for Translational Motion

3.4 Normalization of the Wave function

3.5 Quantized Energy of Translational Motion

3.6 Problems with Solutions

4 Energy of Vibrations

4.1 Hamiltonian of Vibrations

4.2 Solution of the SchrÃ¶dinger equation

4.3 Quantized Energy of Vibrations

4.4 Hermite Polynomials

4.5 Normalization of the Wave Function

4.6 Problems with Solutions

5 Kinetic Energy of Rotations

5.1 Hamiltonian of Rotations

5.1.1 Kinetic Energy and Hamiltonian Operator

5.1.2 Angular Momentum Operator

5.2 Solution of the SchrÃ¶dinger equation

5.3 Quantized Energy of Rotations

5.4 Legendre Polynomials

5.5 Normalization of the Wave function

5.6 Spin Angular Momentum

5.7 Problems with Solutions

Part II THERMODYNAMICS OF SYSTEMS

6 Number of accessible states and Entropy

6.1 Introduction and Definitions

6.2 Calculation of the Number of accessible States

6.2.1 Classical Number of Accessible States

6.2.2 Number of Accessible States for Bosons

6.2.3 Number of Accessible States for Fermions

6.3 Problems with Solutions

7 Equilibrium States of Systems

7.1 Equilibrium Conditions

7.2 Occupation Numbers of Energy Levels

7.3 Concept of Temperature

7.4 Problems with Solutions

8 Thermodynamic Variables

8.1 Free Energy and the Partition Function

8.2 Internal Energy. Caloric State Equation

8.3 Pressure. Thermal State Equation

8.4 Classification of Thermodynamic Variables

8.5 Problems with Solutions

9 Macroscopic Thermodynamics

9.1 Changes of States. Heat and Work

9.2.1 Zeroth Law of Thermodynamics

9.2.2 First Law of Thermodynamics

9.2.3 Second Law of Thermodynamics

9.2.4 Third Law of Thermodynamics

9.3 Open Systems

9.4 Thermal Properties of Systems

9.4.1 Isobaric Expansion

9.4.2 Isochoric Expansion

9.4.3 Isothermal Expansion

9.4.4 Relation between Thermal Coefficients

9.5 Caloric Properties of Systems

9.5.1 Specific Heat at Constant Volume cV

9.5.2 Specific Heat at Constant Pressure cP

9.5.3 Relation between Specific Heats

9.6 Relations between Thermodynamic Coefficients

9.7 Problems with Solutions

10 Variable Number of Particles

10.1 Chemical Potential

10.2 Thermodynamic Potential

10.3 Phases and Phase Equilibrium

10.3.1 Latent Heat

10.3.2 Clausius-Clapeyron Formula

10.4 Problems with Solutions

Part III IDEAL AND NON-IDEAL GASES

11 Ideal Monoatomic Gases

11.1 Continuous Energy Spectrum

11.2 Continuous Partition Function

11.3 Partition Function of Ideal Monoatomic Gases

11.4 Kinetic Theory of Ideal Monoatomic Gases

11.4.1 Maxwell-Boltzmannâs Speed Distribution

11.4.2 Most probable Speed of Gas Particles

11.4.3 Average Speed of Gas Particles

11.4.4 Root-Mean-Square Speed of Gas Particles

11.4.5 Average Kinetic Energy and Internal Energy

11.4.6 Equipartition Theorem

11.5 Thermodynamics of Ideal Monoatomic Gases

11.5.1 Caloric State Equation

11.5.2 Thermal State Equation

11.5.3 Universal and Particular Gas Constants

11.5.4 Caloric and Thermal Coefficients

11.6 Ideal Gases in External Potentials

11.6.1 General Maxwell-Boltzmann distribution

11.6.2 Harmonic and Anharmonic Oscillators

11.6.3 Classical limit of Quantum Partition Function

11.7 Problems with Solutions

12 Ideal Diatomic Gases

12.1 Rotations of Gas Particles

12.2 Vibrations of Gas Particles

12.3 Problems with Solutions

13 Non-ideal Gases

13.1 Partition Function for Non-ideal Gases

13.2 Free Energy of Non-ideal Gases

13.3 Free Energy of Particle Interactions

13.4 Van der Waals Equation

13.5 Caloric State Equation for Non-ideal Gases

13.6 Specific Heats for Non-ideal Gases

13.7 Problems with Solutions

14 Quasi-static Thermodynamic Processes

14.1 Isobaric Process

14.2 Isochoric Process

14.3 Isothermal Process

14.4 Adiabatic Process

14.5 Polytropic Process

14.6 Cyclic Processes. Carnot Cycle

14.7 Problems with Solutions

Part IV QUANTUM STATISTICAL PHYSICS

15 Quantum Distribution Functions

15.1 Entropy Maximization in Quantum Statistics

15.1.1 The Case of Bosons

15.1.2 The Case of Fermions

15.2 Quantum Equilibrium Distribution

15.3 Helmholtz Thermodynamic Potential

15.4 Thermodynamics of Quantum Systems

15.5 Evaluation of Integrals

15.6 Problems with Solutions

16 Electron Gases in Metals

16.1 Ground State of Electron Gases in Metals

16.2 Electron Gases in Metals at Finite Temperatures

16.3 Chemical Potential at Finite Temperatures

16.4 Thermodynamics of Electron Gases

16.5 Problems with Solutions

17 Photon Gas in Equilibrium

17.1 Planck Distribution

17.2 Thermodynamics of Photon Gas in Equilibrium

17.3 Problems with Solutions

18 Other examples of Boson Systems

18.1 Lattice Vibrations and Phonons

18.1.1 Vibration Modes

18.1.2 Internal Energy of Lattice Vibrations

18.2 Bose-Einstein Condensation

18.3 Problems with Solutions

19 Special Topics

19.1 Ultrarelativistic Fermion Gas

19.1.1 Ultrarelativistic Fermion Gas

19.1.2 Ultrarelativistic Fermion Gas

19.2 Thermodynamics of the Expanding Universe

19.2.1 Internal Energy of Elementary-Particle Species

19.2.2 Entropy per Volume Element

19.3 Problems with Solutions

A Physical constants

Bibliography

Index