Application-Driven Quantum and Statistical Physics A Short Course for Future Scientists and Engineers (Essential Textbooks in Physics)

Description

Bridging the gap between traditional books on quantum and statistical physics, this series is an ideal introductory course for students who are looking for an alternative approach to the traditional academic treatment. This pedagogical approach relies heavily on scientific or technological applications from a wide range of fields. For every new concept introduced, an application is given to connect the theoretical results to a real-life situation. Each volume features in-text exercises and detailed solutions, with easy-to-understand applications. Building on the principles introduced in Volume 1, this second volume explains the structure of atoms, the vibration and rotation of molecules. It describes how this is related to thermodynamics through statistical physics. It is shown that these fundamental achievements help to understand how explosives and CO can be detected, what makes a gecko stick to the ceiling, why old stars do not necessarily collapse, where nuclear energy comes from, and more. Readership: Undergraduate students who need a concise introduction to quantum and statistical physics. Graduate students who want to return and learn about the subject from a different perspective. Contents Preface About the Author Part I Model Hamiltonians and Approximations Chapter 1. Vibrating Systems 1.1 On the Role of Harmonic Oscillators in Physics 1.1.1 The pendulum example 1.1.2 A more general perspective 1.2 The Quantum Harmonic Oscillator 1.2.1 The harmonic Hamiltonian 1.2.2 The creation and annihilation operators 1.3 Eigenenergies of the Harmonic Oscillator 1.3.1 Application to the recoilless emission: The principle of Mössbauer spectroscopy 1.4 Wavefunctions for the Harmonic Oscillator 1.5 Discussion and Physical Implications 1.6 Applications to Vibrational Spectroscopies 1.6.1 Pollution monitoring 1.6.2 Detecting explosives 1.7 Coherent States, Quasi-classical States 1.8 Perturbations to Harmonicity 1.8.1 The perturbation theory: A global approach 1.8.2 An application of the second-order perturbation treatment: The London–van der Waals force 1.8.3 Application of the perturbation theory to the anharmonic part of Lennard–Jones’ potential 1.8.4 Application of London–van der Waals forces to atomic force microscopy Chapter 2. Rotating Systems 2.1 The Angular Momentum Operator 2.2 Commutations and Components Incompatibilities 2.3 General Properties of the Angular Momentum Eigenstates and Eigenvalues 2.3.1 Properties ofL2 andLz eigenvalues 2.3.2 Spherical harmonics: The eigenfunctions 2.3.3 Addition of angular momenta 2.4 Applications from Carbon Monoxide to Microwave Ovens Chapter 3. Spin, a New Degree of Freedom 3.1 Stern and Gerlach’s Magnetic Surprise 3.1.1 The Pauli matrices 3.1.2 Spinors and Pauli’s equation 3.2 Indistinguishable Particles and the Pauli Principle 3.2.1 A first wavefunction for several electrons 3.2.2 The Pauli principle 3.3 Application of Pauli’s Principle to Stability Issues: Stars and Nuclei 3.3.1 Pauli’s repulsion and white dwarfs’ stability 3.3.2 Pauli’s principle in the nucleus as a liquid drop Chapter 4. Central Coulombic Potential 4.1 The Hamiltonian of a Hydrogenic System 4.2 Hydrogenic Energies and Wavefunctions 4.3 Applications to Electron Spin Resonance 4.4 Details on the Hydrogenic Radial Function 4.4.1 Asymptotic boundary conditions 4.4.2 Truncated series and eigenenergies 4.4.3 Eigenfunctions for a hydrogenic atom 4.5 Refined Description of the One-Electron Model 4.5.1 “Fine structure” corrections 4.5.2 An application of the “hyperfine” structure Chapter 5. The N-electron Atom 5.1 Optimization of a Trial Wavefunction 5.2 N-electron Atoms: A First Quantum Complexity 5.2.1 A “mean field” approach 5.2.2 When Pauli kicks in 5.3 The Periodic Table of Elements 5.4 Application: The Fluorescent Fingerprint 5.4.1 The fluorescence process 5.4.2 Traces of Archimedes under the gilding Part II Statistical Treatment of Large Assemblies at the Classical Limit Chapter 6. Thermodynamics in the Macroworld 6.1 Laws of Thermodynamics 6.2 Extrema of State Functions: Thermodynamic Potentials 6.3 Equations of State and Maxwell’s Relations 6.3.1 Equation of state and phase transition 6.3.2 Maxwell’s relations 6.3.3 Response functions 6.3.4 Application to ferroelectric and magnetic systems 6.4 Macroequilibria: Phases and Species 6.4.1 Phase diagrams for pure substances 6.4.2 Chemical reactions Chapter 7. Isolated Systems of Particles 7.1 A Large Isolated System: Averages and States 7.1.1 Macroscopic and microscopic states 7.1.2 Gibbs’ averaging and the ergodic principle 7.2 Entropy 7.2.1 Disorder, information and entropy 7.2.2 Assigning probabilities 7.3 Statistical Physics in the Microcanonical Representation 7.3.1 The isolated system: Fixed U, V and N 7.3.2 Connecting statistical and thermodynamic entropies 7.3.3 Counting states, the ideal gas example 7.3.4 Equilibrium conditions from information entropy Chapter 8. Regulated Systems of Classical Particles 8.1 Probability of Microstates 8.2 Partition Functions in Action 8.2.1 The name and the role 8.2.2 Factorizing partition functions 8.2.3 The partition function of a monoatomic ideal gas 8.2.4 The classical approximation 8.2.5 Application to paramagnetism and magnetic cooling 8.2.6 Indistinguishable free particles and the Gibbs paradox 8.3 Applications to the Prediction of Thermodynamics 8.3.1 An important application of partition functions: Equations of state 8.3.2 Application of the canonical partition function: Heat capacities of molecular ideal gases 8.3.3 The chemical potential: Multiple applications of the law of mass action 8.3.4 Application of the grand-canonical approach to catalysis Bibliography Index