The Physics of Atoms and Quanta: Introduction to Experiments and Theory

ISBN-13: 9783642975691 / Angielski / Miękka / 2012 / 467 str.

Hermann Haken; Hans C. Wolf; W. D. Brewer

Opis

This fourth edition contains a few additional figures. Otherwise only typographical er rors have been removed. The final chapter on Fundamentals of the Quantum Theory of Chemical Bonding is continued in an extended way in the textbook Molecular Physics and Elements of Quantum Chemistry by the same authors. This book contains, in particular, a profound presentation of group theory as applied to atoms and molecules. Furthermore, the in teraction between atoms and molecules and light is treated in detail. We thank again Springer-Verlag, in particular Dr. H.1. Kblsch and Mr. C.-D. Bachem for their excellent cooperation as always, and Prof. W. D. Brewer for his con tinuous support in translating our German text. Stuttgart, February 1994 H. Haken H. C. Wolf Preface to the Third Edition The second edition of this book again enjoyed a very positive reception from both uni versity teachers and students. In this edition we have removed all of the typographical errors that came to our attention. In order to keep the book as current as possible, new developments in the direct observation of individual atoms in electromagnetic traps (Paul traps) and of atoms in molecules on solid surfaces using the scanning tunnel microscope have been added to this edition."

Spis treści

1. Introduction.- 1.1 Classical Physics and Quantum Mechanics.- 1.2 Short Historical Review.- 2. The Mass and Size of the Atom.- 2.1 What is an Atom?.- 2.2 Determination of the Mass.- 2.3 Methods for Determining Avogadro’s Number.- 2.3.1 Electrolysis.- 2.3.2 The Gas Constant and Boltzmann’s Constant.- 2.3.3 X-Ray Diffraction in Crystals.- 2.3.4 Determination Using Radioactive Decay.- 2.4 Determination of the Size of the Atom.- 2.4.1 Application of the Kinetic Theory of Gases.- 2.4.2 The Interaction Cross Section.- 2.4.3 Experimental Determination of Interaction Cross Sections.- 2.4.4 Determining the Atomic Size from the Covolume.- 2.4.5 Atomic Sizes from X-Ray Diffraction Measurements on Crystals.- 2.4.6 Can Individual Atoms Be Seen?.- Problems.- 3. Isotopes.- 3.1 The Periodic System of the Elements.- 3.2 Mass Spectroscopy.- 3.2.1 Parabola Method.- 3.2.2 Improved Mass Spectrometers.- 3.2.3 Results of Mass Spectrometry.- 3.2.4 Modern Applications of the Mass Spectrometer.- 3.2.5 Isotope Separation.- Problems.- 4. The Nucleus of the Atom.- 4.1 Passage of Electrons Through Matter.- 4.2 Passage of Alpha Particles Through Matter (Rutherford Scattering).- 4.2.1 Some Properties of Alpha Particles.- 4.2.2 Scattering of Alpha Particles by a Foil.- 4.2.3 Derivation of the Rutherford Scattering Formula.- 4.2.4 Experimental Results.- 4.2.5 What is Meant by Nuclear Radius?.- Problems.- 5. The Photon.- 5.1 Wave Character of Light.- 5.2 Thermal Radiation.- 5.2.1 Spectral Distribution of Black Body Radiation.- 5.2.2 Planck’s Radiation Formula.- 5.2.3 Einstein’s Derivation of Planck’s Formula.- 5.3 The Photoelectric Effect.- 5.4 The Compton Effect.- 5.4.1 Experiments.- 5.4.2 Derivation of the Compton Shift.- Problems.- 6. The Electron.- 6.1 Production of Free Electrons.- 6.2 Size of the Electron.- 6.3 The Charge of the Electron.- 6.4 The Specific Charge e/m of the Electron.- 6.5 Wave Character of Electrons and Other Particles.- 6.6 Interferometry with Atoms.- Problems.- 7. Some Basic Properties of Matter Waves.- 7.1 Wave Packets.- 7.2 Probabilistic Interpretation.- 7.3 The Heisenberg Uncertainty Relation.- 7.4 The Energy-Time Uncertainty Relation.- 7.5 Some Consequences of the Uncertainty Relations for Bound States.- Problems.- 8. Bohr’s Model of the Hydrogen Atom.- 8.1 Basic Principles of Spectroscopy.- 8.2 The Optical Spectrum of the Hydrogen Atom.- 8.3 Bohr’s Postulates.- 8.4 Some Quantitative Conclusions.- 8.5 Motion of the Nucleus.- 8.6 Spectra of Hydrogen-like Atoms.- 8.7 Myionic Atoms.- 8.8 Excitation of Quantum Jumps by Collisions.- 8.9 Sommerfeld’s Extension of the Bohr Model and the Experimental Justification of a Second Quantum Number.- 8.10 Lifting of Orbital Degeneracy by the Relativistic Mass Change.- 8.11 Limits of the Bohr-Sommerfeld Theory. The Correspondence Principle.- 8.12 Rydberg Atoms.- Problems.- 9. The Mathematical Framework of Quantum Theory.- 9.1 The Particle in a Box.- 9.2 The Schrodinger Equation.- 9.3 The Conceptual Basis of Quantum Theory.- 9.3.1 Observations, Values of Measurements and Operators.- 9.3.2 Momentum Measurement and Momentum Probability.- 9.3.3 Average Values and Expectation Values.- 9.3.4 Operators and Expectation Values.- 9.3.5 Equations for Determining the Wavefunction.- 9.3.6 Simultaneous Observability and Commutation Relations.- 9.4 The Quantum Mechanical Oscillator.- Problems.- 10. Quantum Mechanics of the Hydrogen Atom.- 10.1 Motion in a Central Field.- 10.2 Angular Momentum Eigenfunctions.- 10.3 The Radial Wavefunctions in a Central Field*.- 10.4 The Radial Wavefunctions of Hydrogen.- Problems.- 11. Lifting of the Orbital Degeneracy in the Spectra of Alkali Atoms.- 11.1 Shell Structure.- 11.2 Screening.- 11.3 The Term Diagram.- 11.4 Inner Shells.- Problems.- 12. Orbital and Spin Magnetism. Fine Structure.- 12.1 Introduction and Overview.- 12.2 Magnetic Moment of the Orbital Motion.- 12.3 Precession and Orientation in a Magnetic Field.- 12.4 Spin and Magnetic Moment of the Electron.- 12.5 Determination of the Gyromagnetic Ratio by the Einstein-de Haas Method.- 12.6 Detection of Directional Quantisation by Stern and Gerlach.- 12.7 Fine Structure and Spin-Orbit Coupling: Overview.- 12.8 Calculation of Spin-Orbit Splitting in the Bohr Model.- 12.9 Level Scheme of the Alkali Atoms.- 12.10 Fine Structure in the Hydrogen Atom.- 12.11 The Lamb Shift.- Problems.- 13. Atoms in a Magnetic Field: Experiments and Their Semiclassical Description.- 13.1 Directional Quantisation in a Magnetic Field.- 13.2 Electron Spin Resonance.- 13.3 The Zeeman Effect.- 13.3.1 Experiments.- 13.3.2 Explanation of the Zeeman Effect from the Standpoint of Classical Electron Theory.- 13.3.3 Description of the Ordinary Zeeman Effect by the Vector Model.- 13.3.4 The Anomalous Zeeman Effect.- 13.3.5 Magnetic Moments with Spin-Orbit Coupling.- 13.4 The Paschen-Back Effect.- 13.5 Double Resonance and Optical Pumping.- Problems.- 14. Atoms in a Magnetic Field: Quantum Mechanical Treatment.- 14.1 Quantum Theory of the Ordinary Zeeman Effect.- 14.2 Quantum Theoretical Treatment of the Electron and Proton Spins.- 14.2.1 Spin as Angular Momentum.- 14.2.2 Spin Operators, Spin Matrices and Spin Wavefunctions.- 14.2.3 The Schrodinger Equation of a Spin in a Magnetic Field.- 14.2.4 Description of Spin Precession by Expectation Values.- 14.3 Quantum Mechanical Treatment of the Anomalous Zeeman Effect with Spin-Orbit Coupling*.- 14.4 Quantum Theory of a Spin in Mutually Perpendicular Magnetic Fields, One Constant and One Time Dependent.- 14.5 The Bloch Equations.- 14.6 The Relativistic Theory of the Electron. The Dirac Equation.- Problems.- 15. Atoms in an Electric Field.- 15.1 Observations of the Stark Effect.- 15.2 Quantum Theory of the Linear and Quadratic Stark Effects.- 15.2.1 The Hamiltonian.- 15.2.2 The Quadratic Stark Effect. Perturbation Theory Without Degeneracy*.- 15.2.3 The Linear Stark Effect. Perturbation Theory in the Presence of Degeneracy*.- 15.3 The Interaction of a Two-Level Atom with a Coherent Radiation Field.- 15.4 Spin-and Photon Echoes.- 15.5 A Glance at Quantum Electrodynamics*.- 15.5.1 Field Quantization.- 15.5.2 Mass Renormalization and Lamb Shift.- Problems.- 16. General Laws of Optical Transitions.- 16.1 Symmetries and Selection Rules.- 16.1.1 Optical Matrix Elements.- 16.1.2 Examples of the Symmetry Behaviour of Wavefunctions.- 16.1.3 Selection Rules.- 16.1.4 Selection Rules and Multipole Radiation*.- 16.2 Linewidths and Lineshapes.- 17. Many-Electron Atoms.- 17.1 The Spectrum of the Helium Atom.- 17.2 Electron Repulsion and the Pauli Principle.- 17.3 Angular Momentum Coupling.- 17.3.1 Coupling Mechanism.- 17.3.2 LS Coupling (Russell-Saunders Coupling).- 17.3.3 jj Coupling.- 17.4 Magnetic Moments of Many-Electron Atoms.- 17.5 Multiple Excitations.- Problems.- 18. X-Ray Spectra, Internal Shells.- 18.1 Introductory Remarks.- 18.2 X-Radiation from Outer Shells.- 18.3 X-Ray Bremsstrahlung Spectra.- 18.4 Emission Line Spectra: Characteristic Radiation.- 18.5 Fine Structure of the X-Ray Spectra.- 18.6 Absorption Spectra.- 18.7 The Auger Effect.- 18.8 Photoelectron Spectroscopy (XPS), ESCA.- Problems.- 19. Structure of the Periodic System. Ground States of the Elements.- 19.1 Periodic System and Shell Structure.- 19.2 Ground States of Atoms.- 19.3 Excited States and Complete Term Scheme.- 19.4 The Many-Electron Problem. Hartree-Fock Method*.- 19.4.1 The Two-Electron Problem.- 19.4.2 Many Electrons Without Mutual Interactions.- 19.4.3 Coulomb Interaction of Electrons. Hartree and Hartree-Fock Methods.- Problems.- 20. Nuclear Spin, Hyperfine Structure.- 20.1 Influence of the Atomic Nucleus on Atomic Spectra.- 20.2 Spins and Magnetic Moments of Atomic Nuclei.- 20.3 The Hyperfine Interaction.- 20.4 Hyperfine Structure in the Ground States of the Hydrogen and Sodium Atoms.- 20.5 Hyperfine Structure in an External Magnetic Field, Electron Spin Resonance.- 20.6 Direct Measurements of Nuclear Spins and Magnetic Moments, Nuclear Magnetic Resonance.- 20.7 Applications of Nuclear Magnetic Resonance.- 20.8 The Nuclear Electric Quadrupole Moment.- Problems.- 21. The Laser.- 21.1 Some Basic Concepts for the Laser.- 21.2 Rate Equations and Lasing Conditions.- 21.3 Amplitude and Phase of Laser Light.- Problems.- 22. Modern Methods of Optical Spectroscopy.- 22.1 Classical Methods.- 22.2 Quantum Beats.- 22.3 Doppler-free Saturation Spectroscopy.- 22.4 Doppler-free Two-Photon Absorption.- 22.5 Level-Crossing Spectroscopy and the Hanle Effect.- 22.6 Laser Cooling of Atoms.- 23. Fundamentals of the Quantum Theory of Chemical Bonding.- 23.1 Introductory Remarks.- 23.2 The Hydrogen-Molecule Ion H2+.- 23.3 The Tunnel Effect.- 23.4 The Hydrogen Molecule H2.- 23.5 Covalent-Ionic Resonance.- 23.6 The Hund-Mulliken-Bloch Theory of Bonding in Hydrogen.- 23.7 Hybridisation.- 23.8 The ? Electrons of Benzene, C6H6.- Problems.- A. The Dirac Delta Function and the Normalisation of the Wavefunction of a Free Particle in Unbounded Space.- B. Some Properties of the Hamiltonian Operator, Its Eigenfunctions and Its Eigenvalues.- C. Derivation of Heisenberg’s Uncertainty Relation.- Solutions to the Problems.- Bibliography of Supplementary and Specialised Literature.- Fundamental Constants of Atomic Physics (Inside Front Cover).- Energy Conversion Table (Inside Back Cover).

Blurb

The third edition had already been enlarged by the inclusion of new developments such as the direct observation of individual atoms in Paul traps, and of atoms in molecules on solid surfaces using the scanning tunneling microscope. Furthermore, new experiments in atomic interferometry and the possibility of laser cooling of atomic beams were added. The fourth English edition takes minor corrections and additions into account and remains a unique introduction to both experiments and theory of the physics of atoms and quanta. The student will find 160 problems and their solutions, making this book a real study text.