Introductory Quantum Physics And Relativity (Second Edition)

Description

This book is a revised and updated version of Introductory Quantum Physics and Relativity. Based on lectures given as part of the undergraduate degree programme at the University of Leeds, it has been extended in line with recent developments in the field. The book contains all the material required for quantum physics and relativity in the first three years of a traditional physics degree, in addition to more interesting and up-to-date extensions and applications which include quantum field theory, entanglement, and quantum information science. The second edition is unique as an undergraduate textbook as it combines quantum physics and relativity at an introductory level. It expounds the foundations of these two subjects in detail, but also illustrates how they can be combined. It discusses recent applications, but also exposes undergraduates to cutting-edge research topics, such as laser cooling, Bose-Einstein condensation, tunneling microscopes, lasers, nonlocality, and quantum teleportation. Contents Acknowledgements 1 Introduction 2. Old Quantum Theory 2.1. Black body radiation 2.2. The photoelectric effect 2.3. Compton scattering 2.4. De Broglie’s hypothesis 2.5. Bohr’s model of the atom 2.6. Problems with old quantum theory 2.7. Exercises 3. Quantum Mechanics 3.1. Schrodinger’s equation 3.2. Born’s postulate 3.3. Time-independent Schrodinger equation 3.4. Free particle 3.5. Observables and operators 3.6. The superposition principle 3.7. Expectation values 3.8. The uncertainty principle 3.9. Conceptual foundations of quantum mechanics 3.10. Observing the observer 3.11. Exercises 4. Applications of Quantum Mechanics 4.1. Infinite square well 4.2. The quantum harmonic oscillator 4.3. Tunnelling 4.4. Reflection and transmission coefficients 4.5. Tunnelling in action 4.6. Two level systems 4.7. Cold matter 4.8. Exercises 5. Schrodinger Equation in Three Dimensions 5.1. Three-dimensional box 5.2. Schrodinger equation in spherical coordinates 5.3. Separation of variables 5.4. The hydrogen atom 5.5. Radial probability densities 5.6. Exercises 6. Spin and Statistics 6.1. Stern-Gerlach experiment 6.2. What is spin? 6.3. Symmetry of the wave function 6.4. Wave function for two identical particles 6.5. The Pauli Exclusion Principle 6.6. Spin states and spin functions 6.7. Bose–Einstein and Fermi–Dirac distributions 6.8. Exercises 7. Atoms, Molecules and Lasers 7.1. Periodic table 7.2. Ionisation energies 7.3. Energy spectrum 7.4. Ionic bonding 7.5. Covalent bonding 7.6. Van der Waals force 7.7. Lasers 7.8. The lasing condition 7.9. Exercises 8. Formal Structure of Quantum Mechanics 8.1. States and ensembles 8.2. Introduction to Dirac notation 8.3. Operators 8.4. Measurements 8.5. Postulates of quantum mechanics 8.6. Position and momentum operators 8.7. Position and momentum wave functions 8.8. Fourier transforms and the delta function 8.9. Position and momentum operators revisited 8.10. The Schrodinger equation revisited 8.11. The uncertainty principle revisited 8.12. Pure and mixed states 8.13. Annihilation and creation operators 8.14. The Mach–Zehnder interferometer 8.15. Perturbation theory 8.16. Exercises 9. Second Revolution: Relativity 9.1. Simultaneity 9.2. Lorentz transformations 9.3. Length contraction 9.4. Time dilation 9.5. The twin paradox 9.6. Causality 9.7. E = Mc2 9.8. Relativistic Newton’s laws of motion 9.9. General relativity 9.10. Exercises 10. Fine Structure of the Hydrogen Atom 10.1. Relativistic correction to the kinetic energy 10.2. Addition of angular momenta 10.3. Spin-orbit coupling 10.4. The Darwin term 10.5. Lamb shift 10.6. Hyperfine structure 10.6.1. Finite mass effects 10.6.2. Finite volume effects 10.6.3. Nuclear spin 10.7. Zeeman shift 10.8. Stark shift 10.9. Exercises 11. Relativistic Quantum Mechanics 11.1. Why the need for relativistic quantum mechanics? 11.2. The Klein-Gordon equation 11.3. Negative probabilities 11.4. The Dirac equation 11.5. Quantum field theory 11.6. Example: Electron transport in a solid 11.6.1. Low temperature behaviour 11.6.2. High temperature behaviour 11.7. Outlook 11.8. Exercises 12. Quantum Entanglement 12.1. What is entanglement? 12.2. Bell’s inequalities 12.3. Quantum teleportation 12.4. Why is entanglement necessary? 12.5. The non-increase of entanglement under local operations 12.6. Entanglement purification 12.7. Purification of pure states 12.8. Entanglement measures 12.9. Thermodynamics of entanglement 12.10. Quantum computing 12.11. Outlook 12.12. Exercises 13. Solutions 13.1. Chapter 2 13.2. Chapter 3 13.3. Chapter 4 13.4. Chapter 5 13.5. Chapter 6 13.6. Chapter 7 13.7. Chapter 8 13.8. Chapter 9 13.9. Chapter 10 13.10. Chapter 11 13.11. Chapter 12 Bibliography