1. Origins of Quantum Mechanics
    1. A Brief History of Quantum Mechanics
    2. Blackbody Radiation
    3. The Photoelectric Effect
    4. The Compton Effect
    5. de Broglie Matter Waves
    6. Wave-Particle Duality
    7. Probability and Uncertainty in Quantum Mechanics
    8. Atomic Transitions and Spectroscopy
    9. Wave Packets
    10. Summary
  2. Mathematical Tools
    1. Hilbert Space
    2. Dirac Notation
    3. Linear Operators
      1. Basic Properties of Linear Operators
      2. Adjoints and Hermitian Operators
      3. Commutators and Uncertainty Relations
      4. Functions, Inverses, and Unitary Operators
      5. Eigenvalues and Eigenvectors
    4. Representing Operators in Discrete Bases
    5. Fourier Series and Fourier Transforms
    6. Continuous Basis Representations
    7. Summary
  3. Postulates of Quantum Mechanics
    1. Summary of the Basic Postulates
    2. The State Space of a Quantum System
    3. The Schrödinger Equation
    4. Observables as Operators
    5. The Infamous Measurement Postulates
    6. Compatible and Incompatible Observables
    7. The Heisenberg Picture and Conservation Laws
    8. Solving the Schrödinger Equation for Degenerate Hamiltonians
    9. Summary
  4. One Dimensional Problems
    1. The Free Particle
    2. The Infinite Square Well Potential
    3. General Considerations
    4. The Potential Step
    5. The Potential Barrier
    6. The Delta Function Potential
    7. The Finite Square Well Potential
    8. The Harmonic Oscillator
    9. Summary
  5. Angular Momentum
  6. Three Dimensional Problems
  7. The Variational Principle
    1. The Variational Principle