| |
| |
| Preface | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Quantum Description of Systems | |
| |
| |
| |
| Introduction and Basic Concepts | |
| |
| |
| |
| Systems of Identical Particles | |
| |
| |
| |
| Quantum Description of Particles *) | |
| |
| |
| |
| Problems with Solutions *) | |
| |
| |
| |
| Kinetic Energy of Translational Motion | |
| |
| |
| |
| Hamiltonian of Translational Motion | |
| |
| |
| |
| Schr�dinger Equation for Translational Motion *) | |
| |
| |
| |
| Solution of the Schr�dinger Equation *) | |
| |
| |
| |
| Normalization of the Wave Function *) | |
| |
| |
| |
| Quantized Energy of Translational Motion | |
| |
| |
| |
| Problems with Solutions *) | |
| |
| |
| |
| Energy of Vibrations | |
| |
| |
| |
| Hamiltonian of Vibrations | |
| |
| |
| |
| Solution of the Schr�dinger Equation *) | |
| |
| |
| |
| Quantized Energy of Vibrations | |
| |
| |
| |
| Hermite Polynomials *) | |
| |
| |
| |
| Normalization of the Wave Function *) | |
| |
| |
| |
| Problems with Solutions *) | |
| |
| |
| |
| Kinetic Energy of Rotations | |
| |
| |
| |
| Hamiltonian of Rotations | |
| |
| |
| |
| Kinetic Energy and Hamiltonian Operator | |
| |
| |
| |
| Angular Momentum Operator *) | |
| |
| |
| |
| Solution of the Schr�dinger Equation *) | |
| |
| |
| |
| Quantized Energy of Rotations | |
| |
| |
| |
| Legendre Polynomials *) | |
| |
| |
| |
| Normalization of the Wave Function *) | |
| |
| |
| |
| Spin Angular Momentum *) | |
| |
| |
| |
| Problems with Solutions *) | |
| |
| |
| |
| Thermodynamics of Systems | |
| |
| |
| |
| Number of Accessible States and Entropy | |
| |
| |
| |
| Introduction and Definitions | |
| |
| |
| |
| Calculation of the Number of Accessible States | |
| |
| |
| |
| Classical Number of Accessible States | |
| |
| |
| |
| Number of Accessible States for Bosons | |
| |
| |
| |
| Number of Accessible States for Fermions | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Equilibrium States of Systems | |
| |
| |
| |
| Equilibrium Conditions | |
| |
| |
| |
| Occupation Numbers of Energy Levels | |
| |
| |
| |
| Concept of Temperature | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Thermodynamic Variables | |
| |
| |
| |
| Free Energy and the Partition Function | |
| |
| |
| |
| Internal Energy: Caloric-State Equation | |
| |
| |
| |
| Pressure: Thermal-State Equation | |
| |
| |
| |
| Classification of Thermodynamic Variables | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Macroscopic Thermodynamics | |
| |
| |
| |
| Changes of States. Heat and Work | |
| |
| |
| |
| Laws of Thermodynamics | |
| |
| |
| |
| Zeroth Law of Thermodynamics | |
| |
| |
| |
| First Law of Thermodynamics | |
| |
| |
| |
| Second Law of Thermodynamics | |
| |
| |
| |
| Third Law of Thermodynamics | |
| |
| |
| |
| Open Systems | |
| |
| |
| |
| Thermal Properties of Systems | |
| |
| |
| |
| Isobaric Expansion | |
| |
| |
| |
| Isochoric Expansion | |
| |
| |
| |
| Isothermal Expansion | |
| |
| |
| |
| Relation between Thermal Coefficients | |
| |
| |
| |
| Caloric Properties of Systems | |
| |
| |
| |
| Specific Heat at Constant Volume c<sub>V</sub> | |
| |
| |
| |
| Specific Heat at Constant Pressure c<sub>P</sub> | |
| |
| |
| |
| Relation between Specific Heats | |
| |
| |
| |
| Relations between Thermodynamic Coefficients | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Variable Number of Particles | |
| |
| |
| |
| Chemical Potential | |
| |
| |
| |
| Thermodynamic Potential | |
| |
| |
| |
| Phases and Phase Equilibrium | |
| |
| |
| |
| Latent Heat | |
| |
| |
| |
| Clausius-Clapeyron Formula | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Ideal and Nonideal Gases | |
| |
| |
| |
| Ideal Monatomic Gases | |
| |
| |
| |
| Continuous Energy Spectrum | |
| |
| |
| |
| Continuous Partition Function | |
| |
| |
| |
| Partition Function of Ideal Monatomic Gases | |
| |
| |
| |
| Kinetic Theory of Ideal Monatomic Gases | |
| |
| |
| |
| Maxwell-Boltzmann Speed Distribution | |
| |
| |
| |
| Most Probable Speed of Gas Particles | |
| |
| |
| |
| Average Speed of Gas Particles | |
| |
| |
| |
| Root-Mean-Square Speed of Gas Particles | |
| |
| |
| |
| Average Kinetic Energy and Internal Energy | |
| |
| |
| |
| Equipartition Theorem | |
| |
| |
| |
| Thermodynamics of Ideal Monatomic Gases | |
| |
| |
| |
| Caloric-State Equation | |
| |
| |
| |
| Thermal-State Equation | |
| |
| |
| |
| Universal and Particular Gas Constants | |
| |
| |
| |
| Caloric and Thermal Coefficients | |
| |
| |
| |
| Ideal Gases in External Potentials | |
| |
| |
| |
| General Maxwell-Boltzmann Distribution | |
| |
| |
| |
| Harmonic and Anharmonic Oscillators | |
| |
| |
| |
| Classical Limit of Quantum Partition Function | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Ideal Diatomic Gases | |
| |
| |
| |
| Rotations of Gas Particles | |
| |
| |
| |
| Vibrations of Gas Particles | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Nonideal Gases | |
| |
| |
| |
| Partition Function for Nonideal Gases | |
| |
| |
| |
| Free Energy of Nonideal Gases | |
| |
| |
| |
| Free Energy of Particle Interactions | |
| |
| |
| |
| van der Waals Equation | |
| |
| |
| |
| Caloric-State Equation for Nonideal Gases | |
| |
| |
| |
| Specific Heats for Nonideal Gases | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Quasi-Static Thermodynamic Processes | |
| |
| |
| |
| Isobaric Process | |
| |
| |
| |
| Isochoric Process | |
| |
| |
| |
| Isothermal Process | |
| |
| |
| |
| Adiabatic Process | |
| |
| |
| |
| Polytropic Process | |
| |
| |
| |
| Cyclic Processes: Carnot Cycle | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Quantum Statistical Physics | |
| |
| |
| |
| Quantum Distribution Functions | |
| |
| |
| |
| Entropy Maximization in Quantum Statistics | |
| |
| |
| |
| The Case of Bosons | |
| |
| |
| |
| The Case of Fermions | |
| |
| |
| |
| Quantum Equilibrium Distribution | |
| |
| |
| |
| Helmholtz Thermodynamic Potential | |
| |
| |
| |
| Thermodynamics of Quantum Systems | |
| |
| |
| |
| Evaluation of Integrals *) | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Electron Gases in Metals | |
| |
| |
| |
| Ground State of Electron Gases in Metals | |
| |
| |
| |
| Electron Gases in Metals at Finite Temperatures | |
| |
| |
| |
| Chemical Potential at Finite Temperatures | |
| |
| |
| |
| Thermodynamics of Electron Gases | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Photon Gas in Equilibrium | |
| |
| |
| |
| Planck Distribution | |
| |
| |
| |
| Thermodynamics of Photon Gas in Equilibrium | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Other Examples of Boson Systems | |
| |
| |
| |
| Lattice Vibrations and Phonons | |
| |
| |
| |
| Vibration Modes | |
| |
| |
| |
| Internal Energy of Lattice Vibrations | |
| |
| |
| |
| Bose-Einstein Condensation | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Special Topics | |
| |
| |
| |
| Ultrarelativistic Fermion Gas | |
| |
| |
| |
| Ultrarelativistic Fermion Gas for T/T<sub>F</sub> “ 1 | |
| |
| |
| |
| Ultrarelativistic Fermion Gas for T/T<sub>F</sub> ” 1 | |
| |
| |
| |
| Thermodynamics of the Expanding Universe | |
| |
| |
| |
| Internal Energy of Elementary Particle Species | |
| |
| |
| |
| Entropy per Volume Element | |
| |
| |
| |
| Problems with Solutions | |
| |
| |
| |
| Physical Constants | |
| |
| |
| Bibliography | |
| |
| |
| Index | |