Contents

• Course Summary
  • Problems with Classical Physics
  • Thought Experiments on Diffraction
  • Probability Amplitudes
  • Wave Packets and Uncertainty
  • Operators
  • Expectation Values
  • Commutators
  • The Schrödinger Equation
  • Eigenfunctions, Eigenvalues and Vector Spaces
  • A Particle in a Box
  • Piecewise Constant Potentials in One Dimension
  • The Harmonic Oscillator in One Dimension
  • Delta Function Potentials in One Dimension
  • Harmonic Oscillator Solution with Operators
  • More Fun with Operators
  • Two Particles in 3 Dimensions
  • Identical Particles
  • Some 3D Problems Separable in Cartesian Coordinates
  • Angular Momentum
  • Solutions to the Radial Equation for Constant Potentials
  • Hydrogen
  • Solution of the 3D HO Problem in Spherical Coordinates
  • Matrix Representation of Operators and States
  • A Study of Operators and Eigenfunctions
  • Spin 1/2 and other 2 State Systems
  • Quantum Mechanics in an Electromagnetic Field
  • Local Phase Symmetry in Quantum Mechanics and the Gauge Symmetry
  • Addition of Angular Momentum
  • Time Independent Perturbation Theory
  • The Fine Structure of Hydrogen
  • Hyperfine Structure
  • The Helium Atom
  • Atomic Physics
  • Molecules
  • Time Dependent Perturbation Theory
  • Radiation in Atoms
  • Classical Field Theory
  • The Classical Electromagnetic Field
  • Quantization of the EM Field
  • Scattering of Photons
  • Electron Self Energy
  • The Dirac Equation
  • The Dirac Equation
  
  
• The Problems with Classical Physics
  • Black Body Radiation *
  • The Photoelectric Effect
  • The Rutherford Atom *
  • Atomic Spectra *
  • Derivations and Computations
  • Examples
  • Sample Test Problems
  
  
• Diffraction
  • Diffraction from Two Slits
  • Single Slit Diffraction
  • Diffraction from Crystals
  • The DeBroglie Wavelength
  • Wave Particle Duality (Thought Experiments)
  • Examples
  • Sample Test Problems
  
  
• The Solution: Probability Amplitudes
  • Derivations and Computations
  • Sample Test Problems
  
  
• Wave Packets
  • Building a Localized Single-Particle Wave Packet
  • Two Examples of Localized Wave Packets
  • The Heisenberg Uncertainty Principle
  • Position Space and Momentum Space
  • Time Development of a Gaussian Wave Packet *
  • Derivations and Computations
  • Examples
  • Sample Test Problems
  
  
• Operators
  • Operators in Position Space
  • Operators in Momentum Space
  • Expectation Values
  • Dirac Bra-ket Notation
  • Commutators
  • Derivations and Computations
  • Examples
  • Sample Test Problems
  
  
• The Schrödinger Equation
  • Deriving the Equation from Operators
  • The Flux of Probability *
  • The Schrödinger Wave Equation
  • The Time Independent Schrödinger Equation
  • Derivations and Computations
  • Examples
  • Sample Test Problems
  
  
• Eigenfunctions, Eigenvalues and Vector Spaces
  • Eigenvalue Equations
  • Hermitian Conjugate of an Operator
  • Hermitian Operators
  • Eigenfunctions and Vector Space
  • The Particle in a 1D Box
  • Momentum Eigenfunctions
  • Derivations and Computations
  • Examples
  • Sample Test Problems
  
  
• One Dimensional Potentials
  • Piecewise Constant Potentials in 1D
  • The 1D Harmonic Oscillator
  • The Delta Function Potential *
  • The Delta Function Model of a Molecule *
  • The Delta Function Model of a Crystal *
  • The Quantum Rotor
  • Derivations and Computations
  • Examples
  • Sample Test Problems
  
  
• Harmonic Oscillator Solution using Operators
  • Introducing and
  • Commutators of , and
  • Use Commutators to Derive HO Energies
  • Expectation Values of and
  • The Wavefunction for the HO Ground State
  • Examples
  • Sample Test Problems
  
  
• More Fun with Operators
  • Operators in a Vector Space
  • A Complete Set of Mutually Commuting Operators
  • Uncertainty Principle for Non-Commuting Operators
  • Time Derivative of Expectation Values *
  • The Time Development Operator *
  • The Heisenberg Picture *
  • Examples
  • Sample Test Problems
  
  
• Extending QM to Two Particles and Three Dimensions
  • Quantum Mechanics for Two Particles
  • Quantum Mechanics in Three Dimensions
  • Two Particles in Three Dimensions
  • Identical Particles
  • Sample Test Problems
  
  
• 3D Problems Separable in Cartesian Coordinates
  • Particle in a 3D Box
  • The 3D Harmonic Oscillator
  • Sample Test Problems
  
  
• Angular Momentum
  • Rotational Symmetry
  • Angular Momentum Algebra: Raising and Lowering Operators
  • The Angular Momentum Eigenfunctions
  • Derivations and Computations
  • Examples
  • Sample Test Problems
  
  
• The Radial Equation and Constant Potentials *
  • The Radial Equation *
  • Behavior at the Origin *
  • Spherical Bessel Functions *
  • Particle in a Sphere *
  • Bound States in a Spherical Potential Well *
  • Partial Wave Analysis of Scattering *
  • Scattering from a Spherical Well *
  • The Radial Equation for *
  • Sample Test Problems
  
  
• Hydrogen
  • The Radial Wavefunction Solutions
  • The Hydrogen Spectrum
  • Derivations and Calculations
  • Examples
  • Sample Test Problems
  
  
• 3D Symmetric HO in Spherical Coordinates *
• Operators Matrices and Spin
  • The Matrix Representation of Operators and Wavefunctions
  • The Angular Momentum Matrices*
  • Eigenvalue Problems with Matrices
  • An System in a Magnetic Field*
  • Splitting the Eigenstates with Stern-Gerlach
  • Rotation operators for *
  • A Rotated Stern-Gerlach Apparatus*
  • Spin
  • Other Two State Systems*
  • Examples
  • Derivations and Computations
  • Homework Problems
  • Sample Test Problems
  
  
• Homework Problems 130A
  • HOMEWORK 1
  • Homework 2
  • Homework 3
  • Homework 4
  • Homework 5
  • Homework 6
  • Homework 7
  • Homework 8
  • Homework 9
  
  
• Electrons in an Electromagnetic Field
  • Review of the Classical Equations of Electricity and Magnetism in CGS Units
  • The Quantum Hamiltonian Including a B-field
  • Gauge Symmetry in Quantum Mechanics
  • Examples
  • Derivations and Computations
  • Homework Problems
  • Sample Test Problems
  
  
• Addition of Angular Momentum
  • Adding the Spins of Two Electrons
  • Total Angular Momentum and The Spin Orbit Interaction
  • Adding Spin to Integer Orbital Angular Momentum
  • Spectroscopic Notation
  • General Addition of Angular Momentum: The Clebsch-Gordan Series
  • Interchange Symmetry for States with Identical Particles
  • Examples
  • Derivations and Computations
  • Homework Problems
  • Sample Test Problems
  
  
• Time Independent Perturbation Theory
  • The Perturbation Series
  • Degenerate State Perturbation Theory
  • Examples
  • Derivations and Computations
  • Homework Problems
  • Sample Test Problems
  
  
• Fine Structure in Hydrogen
  • Hydrogen Fine Structure
  • Hydrogen Atom in a Weak Magnetic Field
  • Examples
  • Derivations and Computations
  • Homework Problems
  • Sample Test Problems
  
  
• Hyperfine Structure
  • Hyperfine Splitting
  • Hyperfine Splitting in a B Field
  • Examples
  • Derivations and Computations
  • Homework Problems
  • Sample Test Problems
  
  
• The Helium Atom
  • General Features of Helium States
  • The Helium Ground State
  • The First Excited State(s)
  • The Variational Principle (Rayleigh-Ritz Approximation)
  • Variational Helium Ground State Energy
  • Examples
  • Derivations and Computations
  • Homework Problems
  • Sample Test Problems
  
  
• Atomic Physics
  • Atomic Shell Model
  • The Hartree Equations
  • Hund's Rules
  • The Periodic Table
  • The Nuclear Shell Model
  • Examples
  • Homework Problems
  • Sample Test Problems
  
  
• Molecular Physics
  • The Ion
  • The Molecule
  • Importance of Unpaired Valence Electrons
  • Molecular Orbitals
  • Vibrational States
  • Rotational States
  • Examples
  • Derivations and Computations
  • Homework Problems
  • Sample Test Problems
  
  
• Time Dependent Perturbation Theory
  • General Time Dependent Perturbations
  • Sinusoidal Perturbations
  • Examples
  • Derivations and Computations
  • Homework Problems
  • Sample Test Problems
  
  
• Radiation in Atoms
  • The Photon Field in the Quantum Hamiltonian
  • Decay Rates for the Emission of Photons
  • Phase Space: The Density of Final States
  • Total Decay Rate Using Phase Space
  • Electric Dipole Approximation and Selection Rules
  • Explicit 2p to 1s Decay Rate
  • General Unpolarized Initial State
  • Angular Distributions
  • Vector Operators and the Wigner Eckart Theorem
  • Exponential Decay
  • Lifetime and Line Width
  • Phenomena of Radiation Theory
  • Examples
  • Derivations and Computations
  • Homework Problems
  • Sample Test Problems
  
  
• Scattering
  • Scattering from a Screened Coulomb Potential
  • Scattering from a Hard Sphere
  • Homework Problems
  • Sample Test Problems
  
  
• Classical Scalar Fields
  • Simple Mechanical Systems and Fields
  • Classical Scalar Field in Four Dimensions
  • Homework Problems
  
  
• Classical Maxwell Fields
  • Rationalized Heaviside-Lorentz Units
  • The Electromagnetic Field Tensor
  • The Lagrangian for Electromagnetic Fields
  • Gauge Invariance can Simplify Equations
  • Homework Problems
  
  
• Quantum Theory of Radiation
  • Transverse and Longitudinal Fields
  • Fourier Decomposition of Radiation Oscillators
  • The Hamiltonian for the Radiation Field
  • Canonical Coordinates and Momenta
  • Quantization of the Oscillators
  • Photon States
  • Fermion Operators
  • Quantized Radiation Field
  • The Time Development of Field Operators
  • Uncertainty Relations and RMS Field Fluctuations
  • Emission and Absorption of Photons by Atoms
  • Review of Radiation of Photons
  • Black Body Radiation Spectrum
  • Homework Problems
  
  
• Scattering of Photons
  • Resonant Scattering
  • Elastic Scattering
  • Rayleigh Scattering
  • Thomson Scattering
  • Raman Effect
  • Homework Problems
  
  
• Electron Self Energy Corrections
  • The Lamb Shift
  • Homework Problems
  
  
• Dirac Equation
  • Dirac's Motivation
  • The Schrödinger-Pauli Hamiltonian
  • The Dirac Equation
  • The Conserved Probability Current
  • The Non-relativistic Limit of the Dirac Equation
  • Solution of Dirac Equation for a Free Particle
  • ``Negative Energy'' Solutions: Hole Theory
  • Equivalence of a Two Component Theory
  • Relativistic Covariance
  • Parity
  • Bilinear Covariants
  • Constants of the Motion for a Free Particle
  • The Relativistic Interaction Hamiltonian
  • Phenomena of Dirac States
  • Solution of the Dirac Equation for Hydrogen
  • Thomson Scattering
  • Hole Theory and Charge Conjugation
  • Charge Conjugate Waves
  • Quantization of the Dirac Field
  • The Quantized Dirac Field with Positron Spinors
  • Vacuum Polarization
  • The QED LaGrangian and Gauge Invariance
  • Interaction with a Scalar Field
  • Homework Problems
  
  
• Formulas