Quantum Principles and Particles

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication Page
Contents
Preface to the Second Edition
Preface to the First Edition
Section I: Quantum Principles
	1: Perspective and Principles
		1.1 Prelude to Quantum Mechanics
		1.2 Stern–Gerlach Experiment
		1.3 Idealized Stern–Gerlach Results
		1.4 Classical Model Attempts
		1.5 Wave Functions for Two-Physical-Outcomes Cases
		1.6 Measurement Symbols and Completeness
		1.7 Process Diagrams and Operator Properties
		1.8 Operator Reformulation
		1.9 Operator Rotation
		1.10 Bra–Ket Notation/Basis States
		1.11 Transition Amplitudes
		1.12 Three-Magnet Setup Example—Coherence
		1.13 Hermitian Conjugation
		1.14 Unitary Operators
		1.15 A Very Special Operator
		1.16 Matrix Representations
		1.17 Matrix Wave Function Recovery
		1.18 Expectation Values
		1.19 Wrap-Up
		Problems
	2: Particle Motion in One Dimension
		2.1 Photoelectric Effect
		2.2 Compton Effect
		2.3 Uncertainty Relation for Photons
		2.4 Stability of Ground States
		2.5 Bohr Model
		2.6 Fourier Transform and Uncertainty Relations
		2.7 Schrödinger Equation
		2.8 Schrödinger Equation Example
		2.9 Dirac Delta Functions
		2.10 Wave Functions and Probability
		2.11 Probability Current
		2.12 Time Separable Solutions
		2.13 Completeness for Particle States
		2.14 Particle Operator Properties
		2.15 Operator Rules
		2.16 Time Evolution and Expectation Values
		2.17 Wrap-Up
		Problems
	3: Some One-Dimensional Solutions to the Schrödinger Equation
		3.1 Introduction
		3.2 The Infinite Square Well: Differential Solution
		3.3 The Infinite Square Well: Operator Solution
		3.4 The Finite Potential Barrier Step Potential
		3.5 The Harmonic Oscillator
		3.6 The Attractive Kronig–Penney Model
		3.7 Bound State and Scattering Solutions
		Problems
	4: Hilbert Space and Unitary Transformations
		4.1 Introduction and Notation
		4.2 Inner and Outer Operator Products
		4.3 Operator–Matrix Relationship
		4.4 Hermitian Operators and Eigenkets
		4.5 Gram–Schmidt Orthogonalization Process
		4.6 Compatible Operators
		Theorem
		4.7 Uncertainty Relations and Incompatible Operators
		4.8 Simultaneously Measureable Operators
		4.9 Unitary Transformations and Change of Basis
		4.10 Coordinate Displacements and Unitary Transformations
		4.11 Schrödinger and Heisenburg Pictures of Time Evolution
		4.12 Free Gaussian Wave Packet in the Heisenberg Picture
		4.13 Potentials and the Ehrenfest Theorem
		Problems
	5: Three Static Approximation Methods
		5.1 Introduction
		5.2 Time-Independent Perturbation Theory
		5.3 Examples of Time-Independent Perturbation Theory
		5.4 Aspects of Degenerate Perturbation Theory
		5.5 WKB Semiclassical Approximation
		5.6 Use of the WKB Approximation in Barrier Penetration
		5.7 Use of the WKB Approximation in Bound States
		5.8 Variational Methods
		Problems
	6: Generalization to Three Dimensions
		6.1 Cartesian Basis States and Wave Functions in Three Dimensions
		6.2 Position/Momentum Eigenket Generalization
		6.3 Example: Three-Dimensional Infinite Square Well
		6.4 Spherical Basis States
		6.5 Orbital Angular Momentum Operator
		6.6 Effect of Angular Momentum on Basis States
		6.7 Energy Eigenvalue Equation and Angular Momentum
		6.8 Complete Set of Observables for the Radial Schrödinger Equation
		6.9 Specification of Angular Momentum Eigenstates
		6.10 Angular Momentum Eigenvectors and Spherical Harmonics
		6.11 Completeness and Other Properties of Spherical Harmonics
		6.12 Radial Eigenfunctions
		Problems
Section II—Quantum Particles
	7: The Three-Dimensional Radial Equation
		7.1 Recap of the Situation
		7.2 The Free Particle
		7.3 The Infinite Spherical Well Potential
		7.4 The “Deuteron
		7.5 The Coulomb Potential: Initial Considerations
		7.6 The Coulomb Potential: 2-D Harmonic Oscillator Comparison
		7.7 The Confined Coulombic Model
		Problems
	8: Addition of Angular Momenta
		8.1 General Angular-Momentum Eigenstate Properties
		8.2 Combining Angular Momenta for Two Systems
		8.3 Explicit Example of Adding Two Spin-1/2 Systems
		8.4 Explicit Example of Adding Orbital Angular Momentum and Spin 1/2
		8.5 Hydrogen Atom and the Choice of Basis States
		8.6 Hydrogen Atom and Perturbative Energy Shifts
		Problems
	9: Spin and Statistics
		9.1 The Connection between Spin and Statistics
		9.2 Building Wave Functions with Identical Particles
		9.3 Particle Occupation Basis
		9.4 More on Fermi–Dirac Statistics
		9.5 Interaction Operator and Feynman Diagrams
		9.6 Implications of Detailed Balance
		9.7 Density of States Expressions
		9.8 Creating and Destroying Photons
		9.9 Maxwell–Boltzmann Statistics
		9.10 Bose–Einstein Statistics
		9.11 Fermi–Dirac Statistics
		9.12 The Hartree–Fock Equations
		Problems
	10: Time-Dependent Systems
		10.1 Time-Dependent Potentials
		10.2 Sudden and Slow Quantum Transitions
		10.3 Two-State Problems
		10.4 The Berry Phase
		10.5 Magnetic Spin Resonance and the Geometrical Phase
		10.6 The Aharonov–Bohm Effect
		10.7 Time-Dependent Perturbation Theory and Transitions
		10.8 Applications of Fermi’s Golden Rule
		10.9 Exponential Time Decay and Decay Widths
		Problems
	11: Quantum Particle Scattering
		11.1 Introduction
		11.2 The One-Dimensional Integral Schrödinger Equation
		11.3 Reflection and Transmission Amplitudes
		11.4 One-Dimensional Delta-Function Scattering
		11.5 Step-Function Potential Scattering
		11.6 The Born Series
		11.7 The Three-Dimensional Integral Schrödinger Equation
		11.8 The Helmholtz Equation and Plane Waves
		11.9 Cross Sections and the Scattering Amplitude
		11.10 Scattering Phase Shifts
		11.11 Finite-Range Potential Scattering
		11.12 The Three-Dimensional Born Series
		11.13 Identical Particle Scattering
		11.14 Proton–Proton Scattering
		Problems
	12: Connecting to the Standard Model
		12.1 Discrete Symmetries
		12.2 Parity
		12.3 Time Reversal
		12.4 Charge Conjugation
		12.5 Particle Primer
		12.6 Particle Interactions
		12.7 Quantum Electrodynamics
		12.8 Quantum Chromodynamics
		12.9 Weak Interactions
		12.10 Supersymmetry
		12.11 Superstrings
		12.12 Postlude
		12.13 Helpful Books on Particle and String Physics
		Problems
Appendix A: Notation Comments and Comparisons
Appendix B: Lattice Models
Appendix C: 2-D Harmonic Oscillator Wave Function Normalization
Appendix D: Allowed Standard Model Interactions
Appendix E: The Ising Model and More
Appendix F: Weak Flavor Mixing
Appendix G: Quantum Computing
Index