This book offers an introduction to statistical mechanics, special relativity, and quantum physics. It is based on the lecture notes prepared for the one-semester course of "Quantum Physics" belonging to the Bachelor of Science in Material Sciences at the University of Padova. The first chapter briefly reviews the ideas of classical statistical mechanics introduced by James Clerk Maxwell, Ludwig Boltzmann, Willard Gibbs, and others. The second chapter is devoted to the special relativity of Albert Einstein. In the third chapter, it is historically analyzed the quantization of light due to Max Planck and Albert Einstein, while the fourth chapter discusses the Niels Bohr quantization of the energy levels and the electromagnetic transitions. The fifth chapter investigates the Schrodinger equation, which was obtained by Erwin Schrodinger from the idea of Louis De Broglie to associate to each particle a quantum wavelength. Chapter Six describes the basic axioms of quantummechanics, which were formulated in the seminal books of Paul Dirac and John von Neumann. In chapter seven, there are several important application of quantum mechanics: the quantum particle in a box, the quantum particle in the harmonic potential, the quantum tunneling, the stationary perturbation theory, and the time-dependent perturbation theory. Chapter Eight is devoted to the study of quantum atomic physics with special emphasis on the spin of the electron, which needs the Dirac equation for a rigorous theoretical justification. In the ninth chapter, it is explained the quantum mechanics of many identical particles at zero temperature, while in Chapter Ten the discussion is extended to many quantum particles at finite temperature by introducing and using the quantum statistical mechanics. The four appendices on Dirac delta function, complex numbers, Fourier transform, and differential equations are a useful mathematical aid for the reader.

Autorentext

Luca Salasnich is Full Professor of Condensed Matter Theory at the Department of Physics and Astronomy "Galileo Galilei," University of Padova, Italy. He was awarded an M.Sc. in Physics by the University of Padova in 1991, and his Ph.D. in Theoretical Physics by the University of Florence in 1995. 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 200 peer-reviewed scientific papers in international journals, with over 4700 citations.

Inhalt

Table of Contents1 Classical Statistical Mechanics1.1 Kinetic Theory of Gases 1.1.1 Maxwell Distribution of Velocities1.1.2 Maxwell-Boltzmann Distribution of Energies 1.1.3 Single-Particle Density of States 1.2 Statistical Ensembles of Gibbs 1.2.1 Microcanonical Ensemble 1.2.2 Canonical Ensemble 1.2.3 Grand Canonical Ensemble 1.2.4 Many-Particle Density of States 2 Special Relativity 2.1 Lorentz Transformations 2.2 Einstein Postulates 2.2.1 Gedanken Experiment of Einstein 2.3 Relativistic Mechanics 2.3.1 Relativistic Kinematics 2.3.2 Relativistic Dynamics 3 Quantum Properties of Light 3.1 Black-Body Radiation 3.1.1 Ideal Black Body 3.1.2 Derivation of the Planck Law 3.2 Photoelectric E ect 3.2.1 Experimental Data 3.2.2 Theoretical Explanation 3.3 Energy and Linear Momentum of a Photon 3.4 Compton E ect 3.4.1 Theoretical Explanation 4 Quantum Energy Levels of Atoms 4.1 Energy Spectra 4.1.1 Energy Spectrum of Hydrogen Atom 4.2 Hydrogen Atom of Bohr4.2.1 Derivation of the Bohr Results 4.3 Energy Levels and Photons 4.4 Electromagnetic Transitions 5 Wave Properties of Matter 5.1 De Broglie Wavelength 5.1.1 Explaining the Bohr Quantization 5.2 Experiment of Davisson and Germer 5.3 Double-Slit Experiment with Light5.4 Double-Slit Experiment with Electrons 5.5 Old Quantum Mechanics of Bohr, Wilson and Sommerfeld5.6 Matrix Quantum Mechanics of Heisenberg, Born and Jordan 5.7 Wave Quantum Mechanics of Schrodinger 5.7.1 Derivation of the Schr odinger Equation 5.8 Formal Quantization Rules5.8.1 Schrodinger Equation for a Free Particle 5.8.2 Schrodinger Equation for a Particle in an External Potential 5.9 Stationary Schr odinger Equation6 Axioms of Quantum Mechanics 6.1 Matrix Mechanics 6.2 Axioms of Quantum Mechanics7 Applications of Quantum Mechanics 7.1 Quantum Particle in a One-Dimensional Box Potential7.2 Quantum Particle in a One-Dimensional Harmonic Potential8 Quantum Physics of Atoms 8.1 Quantum Particle in a Separable Potential 8.1.1 Quantum Particle in the Harmonic Potential 8.2 Dirac Notation for a Quantum State8.3 Electron in the Hydrogen Atom 8.3.1 Schrodinger Equation in Spherical Polar Coordinates 8.3.2 Selection Rules 8.4 Pauli Exclusion Principle and the Spin8.5 Semi-Integer and Integer Spin: Fermions and Bosons8.6 The Dirac Equation 8.6.1 The Pauli Equation and the Spin8.6.2 Dirac Equation with a Central Potential 8.6.3 Relativistic Hydrogen Atom and Fine Splitting 8.6.4 Relativistic Corrections to the Schrodinger Hamiltonian9 Quantum Mechanics of Many-Body Systems 9.1 Identical Quantum Particles 9.1.1 Spin-Statistics Theorem9.2 Non-Interacting Identical Particles9.2.1 Atomic Shell Structure and the Periodic Table of the Elements 9.3 Interacting Identical Particles9.3.1 Variational Principle9.3.2 Electrons in Atoms and Molecules10 Quantum Statistical Mechanics 10.1 Quantum Statistical Ensembles 10.1.1 Quantum Microcanonical Ensemble 10.1.2 Quantum Canonical Ensemble 10.1.3 Quantum Grand Canonical Ensemble 10.2 Bosons and Fermions at Finite Temperature 10.2.1 Gas of Photons at Thermal Equlibrium10.2.2 Gas of Massive Bosons at Thermal Equlibrium 10.2.3 Gas of Non-Interacting Fermions at Zero TemperatureAppendix A Dirac Delta Function A.1 The Heaviside Step Function A.2 The Strange Function of Dirac A.2.1 Dirac Function and the Integrals A.3 Dirac Function in D Spatial Dimensions Appendix B Complex Numbers B.1 Set of Complex Numbers B.2 Gauss Plane B.2.1 Polar Representation B.3 Euler Formula B.3.1 Proof of the Euler Formula B.3.2 De Moivre FormulaB.4 Fundamental Theorem of Algebra B.5 Complex Functions Appendix C Fourier Transform C.1 Geometric and Taylor SeriesC.2 Fourier Series .C.2.1 Complex Representation of the Fourier Series C.3 Fourier Integral C.3.1 Properties of the Fourier Transform C.3.2 Fourier Transform and Uncertanty TheoremC.4 Fourier Transform of Space-Time FunctionsAppendix D Di erential equations D.1 First-Order Ordinary Di erential EquationsD.1.1 Separation of Variables D.2 Second-Order Ordinary Di erential Equations D.3 Newton Law as a Second-Order ODE D.4 Partial Di erential Equations D.4.1 Wave Equation D.4.2 Di usion Equation Bibliography