The book gives an introduction to the field quantization (second quantization) of light and matter with applications to atomic physics. The first chapter briefly reviews the origins of special relativity and quantum mechanics and the basic notions of quantum information theory and quantum statistical mechanics. The second chapter is devoted to the second quantization of the electromagnetic field, while the third chapter shows the consequences of the light field quantization in the description of electromagnetic transitions.In the fourth chapter it is analyzed the spin of the electron, and in particular its derivation from the Dirac equation, while the fifth chapter investigates the effects of external electric and magnetic fields on the atomic spectra (Stark and Zeeman effects). The sixth chapter describes the properties of systems composed by many interacting identical particles by introducing the Hartree-Fock variational method, the density functional theory, and the Born-Oppenheimerapproximation. Finally, in the seventh chapter it is explained the second quantization of the non-relativistic matter field, i.e. the Schrödinger field, which gives a powerful tool for the investigation of many-body problems and also atomic quantum optics. At the end of each chapter there are several solved problems which can help the students to put into practice the things they learned.

Autorentext

Associate Professor of Condensed Matter Physics at the Department of Physics and Astronomy "Galileo Galilei" of the University of Padova, member of the Scientific Committee of Area 2 (Physical Sciences) of the University of Padova, and president of the B.Sc. in Optics and Optometrics of the University of Padova.

His fields of research are condensed matter theory and statistical physics, in particular nonlinear phenomena and macroscopic quantum effects (like superfluidity and superconductivity) in ultra cold atomic gases and other many-body systems. He has written more than 130 scientific papers in international journals with more than 2500 citations.

Inhalt

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.