Oscillations and Waves: An Introduction

RICHARD E. FITZPATRICK

Published Jan 9, 2013• 14 citations

Abstract

Simple Harmonic Oscillation Massona Spring Simple Harmonic Oscillator Equation LC Circuits Simple Pendula Compound Pendula Damped and Driven Harmonic Oscillation Damped Harmonic Oscillation Quality Factor LCR Circuits Driven Damped Harmonic Oscillation Driven LCR Circuits Transient Oscillator Response Coupled Oscillations Two Spring-Coupled Masses Two Coupled LC Circuits Three Spring-Coupled Masses Transverse Standing Waves Normal Modes of a Beaded String Normal Modes of a Uniform String General Time Evolution of a Uniform String Longitudinal Standing Waves Spring-Coupled Masses Longitudinal Waves on a Thin Elastic Rod Sound Waves in an Ideal Gas Fourier Analysis Traveling Waves Standing Waves in a Finite Continuous Medium Traveling Waves in an Infinite Continuous Medium Wave Interference Energy Conservation Transmission Lines Normal Reflection and Transmission at Interfaces Electromagnetic Waves Doppler Effect Wave Propagation in Inhomogeneous Media Multi-Dimensional Waves Plane Waves Three-Dimensional Wave Equation Cylindrical Waves Spherical Waves Oscillation of an Elastic Sheet Polarization of Electromagnetic Waves Laws of Geometric Optics Fresnel Relations Total Internal Reflection Sound Waves in Fluids Wave Pulses Fourier Transforms General Solution of One-Dimensional Wave Equation Bandwidth Dispersive Waves Pulse Propagation Electromagnetic Waves in Unmagnetized Plasmas Faraday Rotation Electromagnetic Wave Propagation in Conductors Waveguides Pulse Propagation in Two Dimensions Gravity Waves Wave Dragon Ships Ship Wakes Capillary Waves Wave Optics Introduction Two-Slit Interference Coherence Multi-Slit Interference Thin Film Interference One-Dimensional Fourier Optics Single-Slit Diffraction Multi-Slit Diffraction Two-Dimensional Fourier Optics Wave Mechanics Introduction Photoelectric Effect Electron Diffraction Representation of Waves via Complex Numbers Schrodinger's Equation Probability Interpretation of Wavefunction Wave Packets Heisenberg's Uncertainty Principle Wavefunction Collapse Stationary States Three-Dimensional Wave Mechanics Particle in Finite Square Potential Well Square Potential Barrier Appendix A: Physical Constants Appendix B: Useful Mathematics Appendix C: Electromagnetic Theory Bibliography Index Exercises appear at the end of each chapter.

Related papers

Introductory Quantum Mechanics

Rodney C. Greenhow

Part 1: the need for the quantum mechanics quantization of radiation the special theory of relativity wave-particle duality the nature of matter waves the uncertainty principle the Bohr atom. Part 2 Schrodinger's equation: the postulates of quantum mechanics the wave equation the wave equation in three dimensions the time-independent Schrodinger equation stationary states normalisation probability flux physical constraints on the wave-function wave packets Gaussian wave-packets and the uncertainty principle. Part 3 One-dimensional potential wells: potential wells the one-dimensional infinite square well discussion of infinite square-well results eigenvalue equations the finite square well finite square well eigenfunctions the control of the wave-function by the wave equation numerical integration of Schrodinger's equation continuum solutions of the square-well potential interpretation of unbound-particle wave functions the double potential well the quantum bouncer electric fields and the tilted well the harmonic oscillator - introduction the quantum oscillator discussion of harmonic oscillator eigenvalues and eigenfunctions the classical probability density more potential wells. Part 4 Schrodinger's equation in three dimensions: particle in a three dimensional box degeneracy Schrodingers equation in spherical polar coordinates - the hydrogen atom normalisation. Part 5 Formal development of quantum mechanics: eigenvalues equations, operators and measurements the momentum operator, eigenvalues and eigenfunctions the position operator and its eigenfunctions Hermitian operators orthogonality of eigenfunctions the expansion postulate example - the b-decay of tritium expectation values compatibility of observables - commutators non-commuting operators time-dependence of expectation values - Ehrenfest's theorem abstract operators - the parity operator, matrix mechanics. Part 6 Angular momentum: angular momentum operators angular momentum commutators angular momentum eigenvalues and eigenfunctions interpretation of angular momentum eigenvalues interpretation of angular momentum eigenfunctions the Stern-Gerlach apparatus and electron spin spin operators - the Pauli Spin matrices the Zeeman effect measurements in quantum mechanics. Part 7 Spherically symmetric potential wells: the rigid rotator the radial equation the hydrogen atom and hydrogen like ions the isotropic harmonic oscillator molecular vibrations - the Morse potential the spherical square well general properties of spherically symmetric potential wells. (Part contents)

Jan 1, 199015 citations

Quantum Mechanics: Concepts and Applications

Nouredine Zettili

Preface. 1. Origins of Quantum Physics. 1.1 Historical Note. 1.2 Particle Aspect of Radiation. 1.3 Wave Aspect of Particles. 1.4 Particles versus Waves. 1.5 Indeterministic Nature of the Microphysical World. 1.6 Atomic Transitions and Spectroscopy. 1.7 Quantization Rules. 1.8 Wave Packets. 1.9 Concluding Remarks. 1.10 Solved Problems. Exercises. 2. Mathematical Tools of Quantum Mechanics. 2.1 Introduction. 2.2 The Hilbert Space and Wave Functions. 2.3 Dirac Notation. 2.4 Operators. 2.5 Representation in Discrete Bases. 2.6 Representation in Continuous Bases. 2.7 Matrix and Wave Mechanics. 2.8 Concluding Remarks. 2.9 Solved Problems. Exercises. 3. Postulates of Quantum Mechanics. 3.1 Introduction. 3.2 The Basic Postulates of Quantum Mechanics. 3.3 The State of a System. 3.4 Observables and Operators. 3.5 Measurement in Quantum Mechanics. 3.6 Time Evolution of the System's State. 3.7 Symmetries and Conservation Laws. 3.8 Connecting Quantum to Classical Mechanics. 3.9 Solved Problems. Exercises. 4. One-Dimensional Problems. 4.1 Introduction. 4.2 Properties of One-Dimensional Motion. 4.3 The Free Particle: Continuous States. 4.4 The Potential Step. 4.5 The Potential Barrier and Well. 4.6 The Infinite Square Well Potential. 4.7 The Finite Square Well Potential. 4.8 The Harmonic Oscillator. 4.9 Numerical Solution of the Schrodinger Equation. 4.10 Solved Problems. Exercises. 5. Angular Momentum. 5.1 Introduction. 5.2 Orbital Angular Momentum. 5.3 General Formalism of Angular Momentum. 5.4 Matrix Representation of Angular Momentum. 5.5 Geometrical Representation of Angular Momentum. 5.6 Spin Angular Momentum. 5.7 Eigen functions of Orbital Angular Momentum. 5.8 Solved Problems. Exercises. 6. Three-Dimensional Problems. 6.1 Introduction. 6.2 3D Problems in Cartesian Coordinates. 6.3 3D Problems in Spherical Coordinates. 6.4 Concluding Remarks. 6.5 Solved Problems. Exercises. 7. Rotations and Addition of Angular Momenta. 7.1 Rotations in Classical Physics. 7.2 Rotations in Quantum Mechanics. 7.3 Addition of Angular Momenta. 7.4 Scalar, Vector and Tensor Operators. 7.5 Solved Problems. Exercises. 8. Identical Particles. 8.1 Many-Particle Systems. 8.2 Systems of Identical Particles. 8.3 The Pauli Exclusion Principle. 8.4 The Exclusion Principle and the Periodic Table. 8.5 Solved Problems. Exercises. 9. Approximation Methods for Stationary States. 9.1 Introduction. 9.2 Time-Independent Perturbation Theory. 9.3 The Variational Method. 9.4 The Wentzel Kramers Brillou in Method. 9.5 Concluding Remarks. 9.6 Solved Problems. Exercises. 10. Time-Dependent Perturbation Theory. 10.1 Introduction. 10.2 The Pictures of Quantum Mechanics. 10.3 Time-Dependent Perturbation Theory. 10.4 Adiabatic and Sudden Approximations. 10.5 Interaction of Atoms with Radiation. 10.6 Solved Problems. Exercises. 11. Scattering Theory. 11.1 Scattering and Cross Section. 11.2 Scattering Amplitude of Spinless Particles. 11.3 The Born Approximation. 11.4 Partial Wave Analysis. 11.5 Scattering of Identical Particles. 11.6 Solved Problems. Exercises. A. The Delta Function. A.1 One-Dimensional Delta Function. A.2 Three-Dimensional Delta Function. B. Angular Momentum in Spherical Coordinates. B.1 Derivation of Some General. B.2 Gradient and Laplacianin Spherical Coordinates. B.3 Angular Momentum in Spherical Coordinates. C. Computer Code for Solving the Schrodinger Equation. Index.

Oct 1, 200143 citations

The structure of matter : an introduction to quantum mechanics

R. Stephen Berry, Stuart A. Rice, John Ross

PREFACE PART I: THE STRUCTURE OF MATTER 1. THE MICROSCOPIC WORLD: ATOMS AND MOLECULES 1.1 Development of the Atomic Theory: Relative Atomic Weights 1.2 Atomic Magnitudes 1.3 The Charge-to-Mass Ratio of the Electron: Thomson's Method 1.4 The Charge of the Electron: Millikan's Method 1.5 Mass Spectrometry 1.6 The Atomic Mass Scale and the Mole 1.7 The Periodic Table 2. ORIGINS OF THE QUANTUM THEORY OF MATTER 2.1 The Franck-Hertz Experiment 2.2 The Photoelectric Effect 2.3 X-rays and Matter 2.4 The Emission Spectra of Atoms 2.5 The Nuclear Atom 2.6 The Problem of Black-Body Radiation 2.7 The Concept of Action 2.8 The Harmonic Oscillator 2.9 Action Quantized: The Heat Capacity of Solids 2.10 Some Orders of Magnitude 2.11 Bohr's Model of the Atom Appendix 2A: Rutherford Scattering 3. MATTER WAVES IN SIMPLE SYSTEMS 3.1 The de Broglie Hypothesis 3.2 The Nature of Waves 3.3 Dispersion Relations and Wave Equations: The Free Particle 3.4 Operators 3.5 Eigenfunctions and Eigenvalues 3.6 The Particle in a One-Dimensional Box 3.7 The Indeterminacy or Uncertainty Principle 3.8 Expectation Values Summary of Postulates 3.9 Particles in Two- and Three-Dimensional Boxes 3.10 Particles in Circular Boxes 3.11 Particles in Spherical Boxes 3.12 The Rigid Rotor Appendix 3A: More on Circular Coordinates and the Circular Box 4. PARTICLES IN VARYING POTENTIAL FIELDS TRANSITIONS 4.1 Finite Potential Barriers 4.2 The Quantum Mechanical Harmonic Oscillator 4.3 The Hydrogen Atom 4.4 The Shapes of Orbitals 4.5 Transitions between Energy Levels 5. THE STRUCTURE OF ATOMS 5.1 Electron Spin Magnetic Phenomena 5.2 The Pauli Exclusion Principle the Aufbau Principle 5.3 Electronic Configurations of Atoms 5.4 Calculation of Atomic Structures 5.5 Atomic Structure and Periodic Behavior 5.6 Term Splitting and the Vector Model 5.7 Fine Structure and Spin-Orbit Interactions Appendix 5A: The Stern-Gerlach Experiment 6. THE CHEMICAL BOND IN THE SIMPLEST MOLECULES: H[2+ AND H[2 6.1 Bonding Forces between Atoms 6.2 The Simplest Molecule: The Hydrogen Molecule-Ion, H[2+ 6.3 H[2+: Molecular Orbitals and the LCAO Approximation 6.4 H[2+: Obtaining the Energy Curve 6.5 H[2+: Correlation of Orbitals Excited States 6.6 The H[2 Molecule: Simple MO Description 6.7 Symmetry Properties of Identical Particles 6.8 H[2: The Valence Bond Representation 6.9 H[2: Beyond the Simple MO and VB Approximations 6.10 H[2: Excited Electronic States Appendix 6A: Orthogonality Appendix 6B: Hermitian Operators 7. MORE ABOUT DIATOMIC MOLECULES 7.1 Vibrations of Diatomic Molecules 7.2 Rotations of Diatomic Molecules 7.3 Spectra of Diatomic Molecules 7.4 The Ionic Bond 7.5 Homonuclear Diatomic Molecules: Molecular Orbitals and Orbital Correlation 7.6 Homonuclear Diatomic Molecules: Aufbau Principle and Structure of First-Row Molecules 7.7 Introduction to Heteronuclear Diatomic Molecules: Electronegativity 7.8 Bonding in LiH: Crossing and Noncrossing Potential Curves 7.9 Other First-Row Diatomic Hydrides 7.10 Isoelectronic and Other Series Appendix 7A: Perturbation Theory 8. TRIATOMIC MOLECULES 8.1 Electronic Structure and Geometry in the Simplest Cases: H[3 and H[3+ 8.2 Dihydrides: Introduction to the Water Molecule 8.3 Hybrid Orbitals 8.4 Delocalized Orbitals in H[2O: The General MO Method 8.5 Bonding in More Complex Triatomic Molecules 8.6 Normal Coordinates and Modes of Vibration 8.7 A Solvable Example: The Vibrational Modes of CO[2 8.8 Transitions and Spectra of Polyatomic Molecules: Rotations and Vibrations 8.9 Transitions and Spectra of Polyatomic Molecules: Magnetic Transitions 8.10 Transitions and Spectra of Polyatomic Molecules: Electronic Transitions 9. LARGER POLYATOMIC MOLECULES 9.1 Small Molecules 9.2 Catenated Carbon Compounds Transferability 9.3 Other Extended Structures 9.4 Some Steric Effects 9.5 Complex Ions and Other Coordination Compounds: Simple Polyhedra 9.6 Chirality and Optical Rotation 9.7 Chiral and Other Complex Ions 9.8 Magnetic Properties of Complexes 9.9 Electronic Structure of Complexes Appendix 9A: Schmidt Orthogonalization 10. INTERMOLECULAR FORCES 10.1 Long-Range Forces: Interactions between Charge Distributions 10.2 Empirical Intermolecular Potentials 10.3 Weakly Associated Molecules 11. THE STRUCTURE OF SOLIDS 11.1 Some General Properties of Solids 11.2 Space Lattices and Crystal Symmetry 11.3 X-ray Diffraction from Crystals: The Bragg Model 11.4 The Laue Model 11.5 Determination of Crystal Structures 11.6 Techniques of Diffraction 11.7 Molecular Crystals 11.8 Structures of Ionic Crystals 11.9 Binding Energy of Ionic Crystals 11.10 Covalent Solids 11.11 The Free-Electron Theory of Metals 11.12 The Band Theory of Solids 11.13 Conductors, Insulators, and Semiconductors 11.14 Other Forms of Condensed Matter APPENDICES I. Systems of Units II. Partial Derivatives III. Glossary of Symbols IV. Searching the Scientific Literature INDEX

Oxford University Press eBooksJan 1, 20025 citations

Quantum Principles and Particles, Second Edition

Walter Wilcox

QUANTUM PRINCIPLES Perspective and Principles Prelude to Quantum Mechanics Stern-Gerlach Experiment Idealized Stern-Gerlach Results Classical Model Attempts Wave Functions for Two Physical-Outcome Case Process Diagrams, Operators, and Completeness Further Properties of Operators/Modulation Operator Reformulation Operator Rotation Bra-Ket Notation/Basis States Transition Amplitudes Three-Magnet Setup Example-Coherence Hermitian Conjugation Unitary Operators A Very Special Operator Matrix Representations Matrix Wave Function Recovery Expectation Values Wrap Up Problems Free Particles in One Dimension Photoelectric Effect Compton Effect Uncertainty Relation for Photons Stability of Ground States Bohr Model Fourier Transform and Uncertainty Relations Schrodinger Equation Schrodinger Equation Example Dirac Delta Functions Wave Functions and Probability Probability Current Time Separable Solutions Completeness for Particle States Particle Operator Properties Operator Rules Time Evolution and Expectation Values Wrap-Up Problems Some One-Dimensional Solutions to the Schrodinger Equation Introduction The Infinite Square Well: Differential Solution The Infinite Square Well: Operator Solution The Finite Potential Barrier Step Potential The Harmonic Oscillator The Attractive Kronig-Penny Model Bound State and Scattering Solutions Problems Hilbert Space and Unitary Transformations Introduction and Notation Inner and Outer Operator Products Operator-Matrix Relationship Hermitian Operators and Eigenkets Gram-Schmidt Orthogonalization Process Compatible Operators Uncertainty Relations and Incompatible Operators Simultaneously Measureable Operators Unitary Transformations and Change of Basis Coordinate Displacements and Unitary Transformations Schrodinger and Heisenburg Pictures of Time Evolution Free Gaussian Wave Packet in the Heisenberg Picture Potentials and the Ehrenfest Theorem Problems Three Static Approximation Methods Introduction Time-Independent Perturbation Theory Examples of Time-Independent Perturbation Theory Aspects of Degenerate Perturbation Theory WKB Semiclassical Approximation Use of the WKB Approximation in Barrier Penetration Use of the WKB Approximation in Bound States Variational Methods Problems Generalization to Three Dimensions Cartesian Basis States and Wave Functions in Three Dimensions Position/Momentum Eigenket Generalization Example: Three-Dimensional Infinite Square Well Spherical Basis States Orbital Angular Momentum Operator Effect of Angular Momentum on Basis States Energy Eigenvalue Equation and Angular Momentum Complete Set of Observables for the Radial Schrodinger Equation Specification of Angular Momentum Eigenstates Angular Momentum Eigenvectors and Spherical Harmonics Completeness and Other Properties of Spherical Harmonics Radial Eigenfunctions Problems QUANTUM PARTICLES The Three-Dimensional Radial Equation Recap of the Situation The Free Particle The Infinite Spherical Well Potential The Deuteron The Coulomb Potential: Initial Considerations The Coulomb Potential: 2-D Harmonic Oscillator Comparison The Confined Coulombic Model Problems Addition of Angular Momenta General Angular-Momentum Eigenstate Properties Combining Angular Momenta for Two Systems Explicit Example of Adding Two Spin 1/2 Systems Explicit Example of Adding Orbital Angular Momentum and Spin 1/2 Hydrogen Atom and the Choice of Basis States Hydrogen Atom and Perturbative Energy Shifts Problems Spin and Statistics The Connection between Spin and Statistics Building Wave Functions with Identical Particles Particle Occupation Basis More on Fermi-Dirac Statistics Interaction Operator and Feynman Diagrams Implications of Detailed Balance Cubical Enclosures and Particle States Maxwell-Boltzmann Statistics Bose-Einstein Statistics Fermi-Dirac Statistics The Hartree-Fock Equations Problems Quantum Particle Scattering Introduction The One-Dimensional Integral Schrodinger Equation Reflection and Transmission Amplitudes One-Dimensional Delta-Function Scattering Step-Function Potential Scattering The Born Series The Three-Dimensional Integral Schrodinger Equation The Helmholtz Equation and Plane Waves Cross Sections and the Scattering Amplitude Scattering Phase Shifts Finite-Range Potential Scattering The Three-Dimensional Born Series Identical Particle Scattering Proton-Proton Scattering Problems Connecting to the Standard Model Introduction Discrete Symmetries Parity Time Reversal Charge Conjugation Particle Primer Particle Interactions Quantum Electrodynamics Quantum Chromodynamics Weak Interactions Beyond the Standard Model Supersymmetry Superstrings Postlude Helpful Introductory Books on Particle and String Physics More Advanced Books on Particle and String Physics Problems Appendix: Notation Comments and Comparisons Appendix: Lattice Models Appendix: 2-D Harmonic Oscillator Wave Function Normalization Appendix: Allowed Standard Model Interactions Appendix: Weak Flavor Mixing Appendix: The Ising Model and More Index

Aug 27, 20190 citations

Essentials of Photonics

Alan J. Rogers

Photons and ElectronsHistorical SketchThe Wave Nature of LightPolarizationThe Electromagnetic SpectrumEmission and Absorption ProcessesPhoton Statistics The Behaviour of Electrons LasersSummaryWave Properties of LightThe Electromagnetic SpectrumWave RepresentationElectromagnetic WavesReflection and RefractionTotal Internal ReflectionInterference of LightLight WaveguidingInterferometersDiffractionGaussian Beams and Stable Optical ResonatorsPolarization OpticsThe Polarization EllipseCrystal OpticsRetarding WaveplatesA Variable Waveplate: The Soleil-Babinet Compensator Polarizing PrismsLinear BirefringenceCircular BirefringenceElliptical BirefringencePractical Polarization EffectsPolarization AnalysisThe Form of the Jones MatricesLight and Matter Emission, Propagation, and Absorption ProcessesClassical Theory of Light Propagation in Uniform Dielectric Media Optical Dispersion Emission and Absorption of LightOptical Coherence and CorrelationIntroductionMeasure of Coherence Wiener-Khinchin TheoremDual-Beam Interference Practical Examples Some Essential Physics of Radiation and Solids RadiationElectrons in Solids Optical Sources, Modulators, and DetectorsOptical SourcesOptical ModulatorsPhotodetectorsOptical WaveguidesThe Planar Waveguide Integrated OpticsCylindrical WaveguidesOptical FibresOptical Fibres for CommunicationsPolarization-Holding Waveguides Photonic Crystal FibresNonlinear OpticsNonlinear Optics and Optical FibresThe Formalism of Nonlinear OpticsSecond-Harmonic Generation and Phase MatchingOptical MixingIntensity-Dependent Refractive IndexFour-Photon Mixing (FPM)Parametric and Inelastic ProcessesSolitonsPhotosensitivityNon-Linear Effects in Photonic Crystal Fibres (PCF)Photonics in ActionAntireflective Coatings Optical-Fibre Current MeasurementThe Integrated Optical Spectrum AnalyserThe Audio Compact Disc (CD) The Optical-Fibre GyroscopeHolographyOptical-Time-Domain Reflectometry (OTDR) and Its Use in Distributed Optical-Fibre Raman Temperature Sensing (DTS)Measurement of Very Short Optical Pulses: The AutocorrelatorTopics in Optical-Fibre CommunicationsRegimes-Correlation LengthEpilogue And What of the Future?AppendicesAppendix I: Maxwell's EquationsAppendix II: The Fourier Inversion TheoremAppendix III: Symmetry of the Permittivity TensorAppendix IV: The Polarization EllipseAppendix V: Radiation from an Oscillating DipoleAppendix VI: The d-FunctionAppendix VII: The Fermi-Dirac Function Appendix VIII: Second Harmonic Generation Appendix IX: The Sampling TheoremAppendix X: The Semiconductor EquationAppendix XI: The Formal Analysis of Polarization-Mode Dispersion (PMD)ReferencesEach chapter includes an introduction, conclusion, problems, references, and suggestions for further reading.

Dec 5, 20084 citations

Theory of quanta

Iwo Białynicki‐Birula, Marek Cieplak, Jerzy Zdzisław Kamiński +1 more

1: The Birth of Quantum Theory. 1.1: The radiation of an ideal black body. 1.2: Line spectra and Bohr's model of the atom. 1.3: The quantum conditions of Bohr-Sommerfield. 1.4: Waves of matters. Comments. Problems. 2: Classical Physics - Quantum Physics. 2.1: The difficulties of classical theory. 2.2: The successes of quantum theory. 2.3: Problems with interpretation of quantum theory. 2.4: Quantum theory (1930. Problems. II: Schrodinger's Equation and the Interpretation of its Solutions. 3: Schrodinger's Equation. 3.1: The Schrodinger equation with time. 3.2: The time-dependent Schrodinger equation. Comments. Problems. 4: The Probabilistic Interpretation of the Wavefunction. Comments. Problems. 5: The Motion of a Free Particle in Wave Mechanics. 5.1: The spreading of wave packets. 5.2: The initial problem for Schrodinger's free particle equation. 5.3: The Gaussian wave packet. Comments. Problems. 6: The Momentum of a Particle and the Fourier Transformation of the Wavefunction. Comments. Problems. 7: Description of Experiments in Wave Mechanics and the Heinsberg Uncertainty Principle. 7.1: Heisenberg's uncertainty principle. 7.2: The entropic uncertainty principle. Comments. Problems. 8: A Charged Particle in an Electromagnetic Field. Comments. Problems. 9: The Hydrodynamic Formulation of Wave Mechanics. 9.1: The motion of the probability fluid in an electromagnetic field. Comments. Problems. 10: The Spin of the Elctron and Pauli's Equation. 10.1: The magnetic moment vector. 10.2: Pauli's equation. 10.3: The Stern-Gerlach experiments. Comments. Problems. 11: The Hydrodynamic Picture of Wave Mechanics of a Particle with Spin. Comments. Problems. 12: Ehrenfest's Equations. 12.1: A particle with spin in the electromagnetic field. Problems. 13: Descriptiopn of Particle Motion in Phase Space -- Wigner's Function. Comments. Problems. 14: Mixed States. 14.1: An unpolarized beam as a mixed state. Comments. Problems. III: Solutions of Schrodinger's Equation. 15: Classification of Solutions to Schrodinger's Equation. 15.1: Scattering states. 15.2: The completeness of the set of bound and scattering state wavefunctions. 15.3: Orthogonality of the wavefunctions. 15.4: Development of the system in time. 15.5: Bound and scattered states. Problems. 16: Bound States and Energy. 16.1: The three-dimensional spherically symmetric potential well. Comments. Problems. 17: Scattering States and Collision Cross-sections. 17.1: One-dimensional scattering. 17.2: The method of integral equations. 17.3: Three-dimensional scattering. 17.4: The scattering amplitude. 17.5: The S matrix. 17.6: Collision cross-section. 17.7: The optical theorem. Comments. Problems. 18: Partial Waves and Wave Effects in Scattering. 18.1: Phase shifts. 18.2: The spherical potential hump. 18.3: The Ramsauer-Townsend effect. 18.4: The extinction paradox. Comments. Problems. 19: Resonance States. Problems. 20: The Coulomb Potential. 20.1: Bound states. 20.2: Scattering states. Comments. Problems. 21

Oxford University Press eBooksJan 1, 199280 citations