This textbook offers an introduction to statistical mechanics, special relativity, and quantum physics, developed from lecture notes for the "Quantum Physics" course at the University of Padua. Beginning with a brief review of classical statistical mechanics in the first chapter, the book explores special and general relativity in the second chapter. The third chapter delves into the historical analysis of light quantization, while the fourth chapter discusses Niels Bohr''s quantization of energy levels and electromagnetic transitions. The Schrödinger equation is investigated in the fifth chapter. Chapter Six covers applications of quantum mechanics, including the quantum particle in a box, quantum particle in harmonic potential, quantum tunneling, stationary perturbation theory, and time-dependent perturbation theory. Chapter Seven outlines the basic axioms of quantum mechanics. Chapter Eight focuses on quantum atomic physics, emphasizing electron spin and utilizing the Dirac equation for theoretical justification. The ninth chapter explains quantum mechanics principles for identical particles at zero temperature, while Chapter Ten extends the discussion to quantum particles at finite temperature. Chapter Eleven provides insights into quantum information and entanglement, and the twelfth chapter explains the path integral approach to quantum mechanics.

This book is based on lecture notes originally developed for introductory graduate courses offered by the authors at Dartmouth College and the University of Padova. The first two chapters analyze quantum degenerate gases and various cooling and trapping techniques for atoms. The remaining three chapters discuss ultracold atoms as weakly interacting, strongly interacting, and non-interacting coherent systems. The third chapter presents multiple pieces of evidence for quantum degeneracy in Bose and Fermi gases, followed by peculiar features such as superfluidity and the formation of topological defects. The fourth chapter addresses strongly correlated systems, discussing the BCS-BEC crossover in fermionic gases and quantum phase transitions, including their dependence on effective dimensionality. The fifth chapter offers a more specific discussion of quantum coherence in ultracold atoms and their potential as a platform for quantum metrology and quantum emulation. Four appendices provide more quantitative details of theoretical tools used in the last two chapters. Each chapter concludes with problems and a list of more specialized material. The main goal is to introduce interested students to ultracold atom physics research topics and expose scientists working in other areas of frontier physics to this novel and exciting research direction. This book is also intended to complement existing textbooks in standard courses on condensed matter physics, demonstrating how some general elements of the latter can be understood by continuously increasing the interactions between ultracold and quantum degenerate atoms under controlled external conditions.

This compact but exhaustive textbook, now in its significantly revised and expanded second edition, provides an essential introduction to the field quantization of light and matter with applications to atomic physics and strongly correlated systems. Following an initial review of the origins of special relativity and quantum mechanics, individual chapters are devoted to the second quantization of the electromagnetic field and the consequences of light field quantization for the description of electromagnetic transitions. The spin of the electron is then analyzed, with particular attention to its derivation from the Dirac equation. Subsequent topics include the effects of external electric and magnetic fields on the atomic spectra and the properties of systems composed of many interacting identical particles. The book also provides a detailed explanation of the second quantization of the non-relativistic matter field, i.e., the Schrödinger field, which offers a powerful tool for theinvestigation of many-body problems, and of atomic quantum optics and entanglement. Finally, two new chapters introduce the finite-temperature functional integration of bosonic and fermionic fields for the study of macroscopic quantum phenomena: superfluidity and superconductivity. Several solved problems are included at the end of each chapter, helping readers put into practice all that they have learned.

This textbook offers an introduction to statistical mechanics, special relativity, and quantum physics, developed from lecture notes for the "Quantum Physics" course at the University of Padua. Beginning with a brief review of classical statistical mechanics in the first chapter, the book explores special and general relativity in the second chapter. The third chapter delves into the historical analysis of light quantization, while the fourth chapter discusses Niels Bohr''s quantization of energy levels and electromagnetic transitions. The Schrödinger equation is investigated in the fifth chapter. Chapter Six covers applications of quantum mechanics, including the quantum particle in a box, quantum particle in harmonic potential, quantum tunneling, stationary perturbation theory, and time-dependent perturbation theory. Chapter Seven outlines the basic axioms of quantum mechanics. Chapter Eight focuses on quantum atomic physics, emphasizing electron spin and utilizing the Dirac equation for theoretical justification. The ninth chapter explains quantum mechanics principles for identical particles at zero temperature, while Chapter Ten extends the discussion to quantum particles at finite temperature. Chapter Eleven provides insights into quantum information and entanglement, and the twelfth chapter explains the path integral approach to quantum mechanics.

This book is based on lecture notes originally developed for introductory graduate courses offered by the authors at Dartmouth College and the University of Padova. The first two chapters analyze quantum degenerate gases and various cooling and trapping techniques for atoms. The remaining three chapters discuss ultracold atoms as weakly interacting, strongly interacting, and non-interacting coherent systems. The third chapter presents multiple pieces of evidence for quantum degeneracy in Bose and Fermi gases, followed by peculiar features such as superfluidity and the formation of topological defects. The fourth chapter addresses strongly correlated systems, discussing the BCS-BEC crossover in fermionic gases and quantum phase transitions, including their dependence on effective dimensionality. The fifth chapter offers a more specific discussion of quantum coherence in ultracold atoms and their potential as a platform for quantum metrology and quantum emulation. Four appendices provide more quantitative details of theoretical tools used in the last two chapters. Each chapter concludes with problems and a list of more specialized material. The main goal is to introduce interested students to ultracold atom physics research topics and expose scientists working in other areas of frontier physics to this novel and exciting research direction. This book is also intended to complement existing textbooks in standard courses on condensed matter physics, demonstrating how some general elements of the latter can be understood by continuously increasing the interactions between ultracold and quantum degenerate atoms under controlled external conditions.

This compact but exhaustive textbook, now in its significantly revised and expanded second edition, provides an essential introduction to the field quantization of light and matter with applications to atomic physics and strongly correlated systems. Following an initial review of the origins of special relativity and quantum mechanics, individual chapters are devoted to the second quantization of the electromagnetic field and the consequences of light field quantization for the description of electromagnetic transitions. The spin of the electron is then analyzed, with particular attention to its derivation from the Dirac equation. Subsequent topics include the effects of external electric and magnetic fields on the atomic spectra and the properties of systems composed of many interacting identical particles. The book also provides a detailed explanation of the second quantization of the non-relativistic matter field, i.e., the Schrödinger field, which offers a powerful tool for theinvestigation of many-body problems, and of atomic quantum optics and entanglement. Finally, two new chapters introduce the finite-temperature functional integration of bosonic and fermionic fields for the study of macroscopic quantum phenomena: superfluidity and superconductivity. Several solved problems are included at the end of each chapter, helping readers put into practice all that they have learned.