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• About the Author
• Contents at a Glance
• Table of Contents
• Introduction
• About This Book
• Conventions Used in This Book
• Foolish Assumptions
• How This Book Is Organized
• Icons Used in This Book
• Where to Go from Here
• Part I: Small World, Huh? Essential Quantum Physics
• Chapter 1: Discoveries and Essential Quantum Physics
• Being Discrete: The Trouble with Black-Body Radiation
• The First Pieces: Seeing Light as Particles
• A Dual Identity: Looking at Particles as Waves
• You Can’t Know Everything (But You Can Figure the Odds)
• Chapter 2: Entering the Matrix: Welcome to State Vectors
• Creating Your Own Vectors in Hilbert Space
• Making Life Easier with Dirac Notation
• Grooving with Operators
• Going Hermitian with Hermitian Operators and Adjoints
• Forward and Backward: Finding the Commutator
• Starting from Scratch and Ending Up with Heisenberg
• Eigenvectors and Eigenvalues: They’re Naturally Eigentastic!
• Preparing for the Inversion: Simplifying with Unitary Operators
• Comparing Matrix and Continuous Representations
• Part II: Bound and Undetermined: Handling Particles in Bound States
• Chapter 3: Getting Stuck in Energy Wells
• Looking into a Square Well
• Trapping Particles in Potential Wells
• Trapping Particles in Infinite Square Potential Wells
• Limited Potential: Taking a Look at Particles and Potential Steps
• Hitting the Wall: Particles and Potential Barriers
• Particles Unbound: Solving the Schrödinger Equation for Free Particles
• Chapter 4: Back and Forth with Harmonic Oscillators
• Grappling with the Harmonic Oscillator Hamiltonians
• Creation and Annihilation: Introducing the Harmonic Oscillator Operators
• Finding the Eigenstates
• Looking at Harmonic Oscillator Operators as Matrices
• A Jolt of Java: Using Code to Solve the Schrödinger Equation Numerically
• Part III: Turning to Angular Momentum and Spin
• Chapter 5: Working with Angular Momentum on the Quantum Level
• Ringing the Operators: Round and Round with Angular Momentum
• Finding Commutators of Lx, Ly, and Lz
• Creating the Angular Momentum Eigenstates
• Finding the Angular Momentum Eigenvalues
• Finding the Eigenvalues of the Raising and Lowering Operators
• Interpreting Angular Momentum with Matrices
• Rounding It Out: Switching to the Spherical Coordinate System
• Chapter 6: Getting Dizzy with Spin
• The Stern-Gerlach Experiment and the Case of the Missing Spot
• Getting Down and Dirty with Spin and Eigenstates
• Halves and Integers: Saying Hello to Fermions and Bosons
• Spin Operators: Running Around with Angular Momentum
• Working with Spin 1/2 and Pauli Matrices
• Part IV: Multiple Dimensions: Going 3D with Quantum Physics
• Chapter 7: Rectangular Coordinates: Solving Problems in Three Dimensions
• The Schrödinger Equation: Now in 3D!
• Solving Three-Dimensional Free Particle Problems
• Getting Squared Away with 3D Rectangular Potentials
• Springing into 3D Harmonic Oscillators
• Chapter 8: Solving Problems in Three Dimensions: Spherical Coordinates
• A New Angle: Choosing Spherical Coordinates Instead of Rectangular
• Taking a Good Look at Central Potentials in 3D
• Handling Free Particles in 3D with Spherical Coordinates
• Handling the Spherical Square Well Potential
• Getting the Goods on Isotropic Harmonic Oscillators
• Chapter 9: Understanding Hydrogen Atoms
• Coming to Terms: The Schrödinger Equation for the Hydrogen Atom
• Simplifying and Splitting the Schrödinger Equation for Hydrogen
• Solving for (R)
• Solving for (r)
• Calculating the Energy Degeneracy of the Hydrogen Atom
• Hunting the Elusive Electron
• Chapter 10: Handling Many Identical Particles
• Many-Particle Systems, Generally Speaking
• A Super-Powerful Tool: Interchange Symmetry
• Floating Cars: Tackling Systems of Many Distinguishable Particles
• Juggling Many Identical Particles
• Building Symmetric and Antisymmetric Wave Functions
• Working with Identical Noninteracting Particles
• It’s Not Come One, Come All: The Pauli Exclusion Principle
• Figuring out the Periodic Table
• Part V: Group Dynamics: Introducing Multiple Particles
• Chapter 11: Giving Systems a Push: Perturbation Theory
• Introducing Time-Independent Perturbation Theory
• Working with Perturbations to Nondegenerate Hamiltonians
• Perturbation Theory to the Test: Harmonic Oscillators in Electric Fields
• Working with Perturbations to Degenerate Hamiltonians
• Testing Degenerate Perturbation Theory: Hydrogen in Electric Fields
• Chapter 12: Wham-Blam! Scattering Theory
• Introducing Particle Scattering and Cross Sections
• Translating between the Center-of-Mass and Lab Frames
• Tracking the Scattering Amplitude of Spinless Particles
• The Born Approximation: Rescuing the Wave Equation
• Part VI: The Part of Tens
• Chapter 13: Ten Quantum Physics Tutorials
• An Introduction to Quantum Mechanics
• Quantum Mechanics Tutorial
• Grains of Mystique: Quantum Physics for the Layman
• Quantum Physics Online Version 2.0
• Todd K. Timberlake’s Tutorial
• Physics 24/7’s Tutorial
• Stan Zochowski’s PDF Tutorials
• Quantum Atom Tutorial
• College of St. Benedict’s Tutorial
• A Web-Based Quantum Mechanics Course
• Chapter 14: Ten Quantum Physics Triumphs
• Wave-Particle Duality
• The Photoelectric Effect
• Postulating Spin
• Differences between Newton’s Laws and Quantum Physics
• Heisenberg Uncertainty Principle
• Quantum Tunneling
• Discrete Spectra of Atoms
• Harmonic Oscillator
• Square Wells
• Schrödinger’s Cat
• Glossary
• Index