Courses in Quantum Mechanics

• Introduction
  • Intended audience
  • Major Sources
  • Aim of Course
  • Outline of Course
• Probability Theory
  • Introduction
  • What is Probability?
  • Combining Probabilities
  • Mean, Variance, and Standard Deviation
  • Continuous Probability Distributions
    • Exercises
• Wave-Particle Duality
  • Introduction
  • Wavefunctions
  • Plane Waves
  • Representation of Waves via Complex Functions
  • Classical Light Waves
  • Photoelectric Effect
  • Quantum Theory of Light
  • Classical Interference of Light Waves
  • Quantum Interference of Light
  • Classical Particles
  • Quantum Particles
  • Wave Packets
  • Evolution of Wave Packets
  • Heisenberg's Uncertainty Principle
  • Schrödinger's Equation
  • Collapse of the Wave Function
    • Exercises
• Fundamentals of Quantum Mechanics
  • Introduction
  • Schrödinger's Equation
  • Normalization of the Wavefunction
  • Expectation Values and Variances
  • Ehrenfest's Theorem
  • Operators
  • Momentum Representation
  • Heisenberg's Uncertainty Principle
  • Eigenstates and Eigenvalues
  • Measurement
  • Continuous Eigenvalues
  • Stationary States
    • Exercises
• One-Dimensional Potentials
  • Introduction
  • Infinite Potential Well
  • Square Potential Barrier
  • WKB Approximation
  • Cold Emission
  • Alpha Decay
  • Square Potential Well
  • Simple Harmonic Oscillator
    • Exercises
• Multi-Particle Systems
  • Introduction
  • Fundamental Concepts
  • Non-Interacting Particles
  • Two-Particle Systems
  • Identical Particles
    • Exercises (N.B. Neglect spin in the following questions.)
• Three-Dimensional Quantum Mechanics
  • Introduction
  • Fundamental Concepts
  • Particle in a Box
  • Degenerate Electron Gases
  • White-Dwarf Stars
    • Exercises
• Orbital Angular Momentum
  • Introduction
  • Angular Momentum Operators
  • Representation of Angular Momentum
  • Eigenstates of Angular Momentum
  • Eigenvalues of 
  • Eigenvalues of 
  • Spherical Harmonics
    • Exercises
• Central Potentials
  • Introduction
  • Derivation of Radial Equation
  • Infinite Spherical Potential Well
  • Hydrogen Atom
  • Rydberg Formula
    • Exercises
• Spin Angular Momentum
  • Introduction
  • Spin Operators
  • Spin Space
  • Eigenstates of  and 
  • Pauli Representation
  • Spin Precession
    • Exercises
• Addition of Angular Momentum
  • Introduction
  • General Principles
  • Angular Momentum in the Hydrogen Atom
  • Two Spin One-Half Particles
    • Exercises
• Time-Independent Perturbation Theory
  • Introduction
  • Improved Notation
  • Two-State System
  • Non-Degenerate Perturbation Theory
  • Quadratic Stark Effect
  • Degenerate Perturbation Theory
  • Linear Stark Effect
  • Fine Structure of Hydrogen
  • Zeeman Effect
  • Hyperfine Structure
• Time-Dependent Perturbation Theory
  • Introduction
  • Preliminary Analysis
  • Two-State System
  • Spin Magnetic Resonance
  • Perturbation Expansion
  • Harmonic Perturbations
  • Electromagnetic Radiation
  • Electric Dipole Approximation
  • Spontaneous Emission
  • Radiation from a Harmonic Oscillator
  • Selection Rules
  •  Transitions in Hydrogen
  • Intensity Rules
  • Forbidden Transitions
• Variational Methods
  • Introduction
  • Variational Principle
  • Helium Atom
  • Hydrogen Molecule Ion
• Scattering Theory
  • Introduction
  • Fundamentals
  • Born Approximation
  • Partial Waves
  • Determination of Phase-Shifts
  • Hard Sphere Scattering
  • Low Energy Scattering
  • Resonances
• About this document ...

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Richard Fitzpatrick 2010-07-20