Quantum Physics of Light and Matter: A Modern Introduction to Photons, Atoms and Many-Body Systems

The Origins of Modern Physics.- Special Relativity.- Quantum Mechanics.- Axioms of Quantum Mechanics.- Quantum Information.- Quantum Statistical Mechanics.- Microcanonical Ensemble.- Canonical ensemble.- Grand canonical ensemble Solved Problems.- Second Quantization of Light Electromagnetic Waves.- First Quantization of Light Electromagnetic Potentials and Coulomb Gauge.- Second Quantization of Light.- Fock vs Coherent States for the Light Field.- Linear and Angular Momentum of the Radiation Field.- Zero-Point Energy and the Casimir Effect.- Quantum Radiation Field at Finite Temperature.- Phase Operators.- Solved Problems.- Electromagnetic Transitions.- Classical Electrodynamics.- Quantum Electrodynamics in the Dipole Approximation.- Spontaneous Emission Absorption.- Stimulated Emission.- Einstein Coefficients.- Rate equations for two-level and three-level systems.- Selection Rules.- Life-Time and Natural Line-Width.- Collisional Broadening Doppler Broadening.- Minimal Coupling and Center of Mass.- Solved Problems.- The Spin of the Electron.- The Dirac Equation.- The Pauli Equation and the Spin.- Dirac equation with a central potential Relativistic Hydrogen Atom and Fine splitting.- Relativistic Corrections to the Schrodinger Hamiltonian Solved Problems.- Energy Splitting and Shift due to External Fields.- Stark Effect Zeeman Effect.- Normal Zeeman Effect.- Anomalous Zeeman Effect.- Solved Problems Many-Body Systems.- Identical Quantum Particles.- Non-Interacting Identical Particles.- Uniform Gas of Non-Interacting Fermions.- Atomic Shell Structure and the Periodic Table of the Elements.- Interacting Identical Particles.- Variational Principle.- Hartree for Bosons.- Hartree-Fock for Fermions.- Mean-Field Approximation.- Density Functional Theory.- Molecules and the Born-Oppenheimer Approximation.- Solved Problems.- Second Quantization of Matter.- Schrodinger Field.- Second Quantization of the Schrodinger Field.- Bosonic and Fermionic Matter Field Connection between First and Second.- Quantization Fock vs Coherent states for the Bosonic Matter Field.- Quantum Matter Field at Finite Temperature.- Matter-Radiation Interaction Cavity quantum electrodynamics Bosons in a double-well potential Solved Problems Appendix A Dirac Delta Function.- Appendix B Fourier Transform.- Appendix C Laplace Transform.- Bibliography.