Wave-Particle Duality and Schroedinger Equation. 2. Introduction to Bound States. 3. Rotationally Invariant Potentials: Hydrogen Atom and Beyond. 4. Wave Packets and Uncertainty Relations. 5. Scattering by Simple Barriers. 6. WKB Approximations. 7. Expectation Values and Operators. 8. Electrons in a Magnetic Field. 9. Beyond Hermitian Operators. 10. Harmonic Oscillator: Full Operator Treatment. 11. Composite Systems. 12. Variational Principle. 13. Expansion Principle and Matrix Formulation. 14. Perturbation Theory, I: Degenerate Perturbation Theory. 15. Perturbation Theory, II: Non-Degenerate Perturbation Theory. 16. Symmetry. 17. Electrons in Periodic Crystal Potentials. 18. Rotational Invariance and Angular Momentum. 19. Time-Dependent Perturbation Theory. 20. Elements of Field Quantization. 21. Electron Spin. 22. Indistinguishable Particles: Fermions and Bosons. Appendices: Dirac ...d-Function. Poisson-Distributed Events. Spherical Harmonics. Hydrogen Radial Eigenfunctions. Fourier Integral. Construction of Two Group Character Tables. Selected General References. Fundamental Constants. Index.
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)
BRIEF REVIEW OF CLASSICAL THEORIES Harmonic Oscillator Boltzmann Transport Equation Maxwell's Equations MILESTONE DISCOVERIES AND OLD QUANTUM THEORY Blackbody Radiation and Quantum of Energy Specific Heat of Solids Photoelectric Effects Compton Scattering Duality of Matter Bohr?s H-Atom Theory SCHRODINGER EQUATION AND OPERATOR ALGEBRA Schrodinger Equation Momentum Eigenfunction and Fourier Series Hermitian Operator and Bra Ket Notations Orthgonality and Completeness of Eigenfunctions Basic Postulates of Quantum Mechanics Commutation Relations Conjugate Variables and Uncertainty Relation Operator Equation of Motion and Ehrenfest Theorem PARTICLE IN POTENTIAL WELL Infinite Square Well Potential Particle in 3-D Box Density of States: 1-D, 2-D and 3-D Particle in Quantum Well Particle in Delta Function Potential Well Quantum Well and Wire SCATTERING OF A PARTICLE AT 1-D POTENTIALS Scattering at Step Potential Scattering at Quantum Well TUNNELING AND ITS APPLICATIONS Tunneling across Square Potential Barrier Fowler-Nordheim and Direct Tunneling Resonant Tunneling The Applications of Tunneling PERIODIC POTENTIALS AND ENERGY BANDS 1-D Crystal and Kronig-Penny Model E-k Dispersion and Energy Bands Energy Bands and Resonant Tunneling THE HARMONIC OSCILLATOR Energy Eigenequation The Properties of Energy Eigenfunction The Operator Treatment THE ANGULAR MOMENTUM Angualr Momentum Operators Eigenfunctions and Spherical Harmonics THE HYDROGEN ATOM: THE SCHRODINGER TREATMENT Two-Body Central Force Problem The Hydrogen Atom The Atomic Orbital Virial Theorm and Doppler Shift SYSTEM OF IDENTICAL PARTICLES AND MANY-ELECTRON ATOMS Two Electron System Two Spin 1/2 System The Helium Atom The Periodic Table and the Structure of Atoms MOLECULES AND CHEMICAL BONDS The Ionized Hydrogen Molecule The Hydrogen Molecule Ionic Bond and Van der Waals Attraction THE PERTURBATION THEORY Time Independent Perturbation in Non-Degenerate Systems Time Dependent Perturbation Theory ATOM - FIELD INTERACTION Field Quantization Atom - Field Interaction Driven, Damped Two Level Atom INTERACTION BETWEEN EM WAVES AND OPTICAL MEDIA Attenuation and Dispersion of Waves Density Matrix and Ensemble Averaging Laser Devices QUANTUM STATISTICS General Background and Three Kinds of Particles Statistics for Distinguishable particles Statistics for Fermions and Fermi Distribution Function Statistics for Boson and Bose Einstein Distribution SEMICONDUCTOR STATISTICS Carrier Densities in Intrinsic Semiconductors Carrier Densities in Extrinsic Semiconductors Fermi Level in Extrinsic Semiconductors CHARGE TRANSPORT IN SEMICONDUCTORS Drift and Diffusion Currents Transport Coefficients Equilibrium and Non-Equilibrium Recombination and Generation Currents P-N JUNCTION DIODE The Junction Interface in Equilibrium The Junction Interface Under Bias The Diode I-V Applications of P-N Junction Diodes THE BIPOLAR JUNCTION TRANSISTOR: DEVICE PHYSICS AND TECHNOLOGY Bipolar Junction Transistor: Overview The Physics of Transistor Action Ebers Moll Equations Base Transit Time and Charge Control Model METAL OXIDE SILICON FIELD EFFECT TRANSISTORS (MOSFET) I: OVERVIEW OF DEVICE BEHAVIOR AND APPLICATIONS MOSFET: Overview Charge Control and Metal-Oxide-Silicon System NMOS I-V Applications of MOSFET METAL OXIDE SILICON FIELD EFFECT TRANSISTORS (MOSFET) II: DEVICE SCALING AND SCHOTTKY CONTACT Device Scaling: Physical issues and Limitations Metal - Semiconductor Contacts The I-V Behavior in Metal - Semiconductor Contacts
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.
Table of Contents 1. The Origins of Quantum Mechanics 1.1 Introduction 1.2 Blackbody Radiation The Problem with Blackbody Radiation 1.3 The Nature of Light The Photoelectric Effect The Compton Effect Is it a Particle or a Wave? 1.4 TheWave Nature of Matter 1.5 The Bohr Atom 1.6 Where do we Stand? 2. Math Interlude A: Complex Numbers and Linear Operators 2.1 Complex Numbers 2.2 Operators Definition of an Operator Eigenfunctions and Eigenvalues 3. The Schrodinger Equation 3.1 Derivation of the Schrodinger Equation 3.2 The Meaning of theWave Function 3.3 The Time-Independent Schrodinger Equation Derivation of the Time-Independent Schrodinger Equation Qualitative Solutions and the Origin of Quantization 4. One-Dimensional Time-Independent Schrodinger Equation 4.1 Unbound States: Scattering and Tunneling Scattering From Step-Function Potentials 4.2 Bound Systems The Infinite SquareWell The Harmonic Oscillator Potential 5. Math Interlude B: Linear Algebra 5.1 Properties of Linear Operators 5.2 Vector Spaces Inner Products Adjoint and Hermitian Operators Basis Sets 6. The Three-Dimensional Time-Independent Schrodinger Equation 6.1 Solution in Rectangular Coordinates 6.2 Angular Momentum 6.3 The Schrodinger Equation in Spherical Coordinates 6.4 The Hydrogen Atom 7. Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function 7.1 The Matrix Formulation of Linear Operators 7.2 Dirac Notation 7.3 The Dirac Delta Function 8. Spin Angular Momentum 8.1 Spin Operators 8.2 Evidence for Spin 8.3 Adding Angular Momentum 8.4 The Matrix Representation of Spin 8.5 The Stern-Gerlach Experiment 8.6 Spin Precession 8.7 Spin Systems with Two Particles Noninteracting Spins Interacting Spins 8.8 Measurement Theory Hidden Variables The ManyWorlds Interpretation of Quantum Mechanics 9. Time-Independent Perturbation Theory 9.1 Derivation of Time-Independent Perturbation Theory 9.2 Perturbations to the Atomic Energy Levels Fine Structure The Lamb Shift 9.3 The Atom in External Electric or Magnetic Fields The Atom in an Electric Field: The Stark Effect The Atom in a Magnetic Field: The Zeeman Effect 10. The Variational Principle 10.1 Variational Principle: Theory 10.2 Variational Principle: Application to the Helium Atom 11. Time-Dependent Perturbation Theory 11.1 Derivation of Time-Dependent Perturbation Theory 11.2 Application: Selection Rules for Electromagnetic Radiation 12. Scattering Theory 12.1 Definition of the Cross Section 12.2 The Born Approximation 12.3 PartialWaves 13. The Multiparticle Schrodinger Equation 13.1 Wave Function for Identical Particles 13.2 Multielectron Atoms 14. Some Modern Applications of Quantum Mechanics 14.1 Magnetic Resonance Imaging 14.2 Quantum Computing 15. What Comes Next? Relativistic Quantum Mechanics 15.1 The Klein-Gordon Equation Derivation of the Klein-Gordon Equation Probability Densities and Currents 15.2 The Dirac Equation Answers and Hints for Selected End-of-Chapter Exercises Index
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
(NOTE: All chapters conclude with Final Thoughts, and Exercises and Problems most also include Annotated Selected Readings.)I. WHAT'S IT ALL ABOUT?: A QUALITATIVE INTRODUCTION. 1. Introductory: Why Quantum Physics? 2. Into the Microworld: Duality and the Double Slit. II. STARTING FROM SCRATCH. 3. First Postulates: The State Function and Its Interpretation. 4. An Illustrative Interlude: Wave Packets in One Dimension. 5. Observables in Quantum Physics: A Pragmatist's Approach. 6. A Quantum Equation of Motion: The Schroedinger Equation At Last. 7. Simplifying Matters: The Time-Independent Schroedinger Equation. III. EXAMPLES, EXAMPLES, EXAMPLES. 8. States of a Particle in One Dimension I: Mainly Piecewise-Constant Potentials. 9. States of a Particle in One Dimension II: Mainly Continuous Potentials. IV. TOOLS OF THE TRADE MORE FORMALISM. 10. Operators in Quantum Mechanics I: The Importance of Being Hermitian. 11. Operators in Quantum Mechanics II: To Commute or Not to Commute. 12. Eigenfunction Expansions: How to Solve Any Problem in Quantum Mechanics. 13. Altered States: The Great Measurement Mystery. Appendixes. A. SI Units (The International System of Units. B. Fundamental Constants in SI (and CGS) Units. C. Order-of-Magnitude Estimates. D. Conversion Tables. E. Prefix Dictionary. F. A User's Guide to Atomic Units. G. The Greek Alphabet. H. Handy Trigonometric identities. I. Integrals You Should Know. J. Integrals Involving the Gaussian Function. K. Review of Complex Numbers. L. The Dirac Delta Function. Bibliography. Index.