Contents

• • • Introduction
      • Intended audience
      • Major sources
      • Aim of course
      • Outline of course
  
  
• Fundamentals
  • Probability theory
    • Introduction
    • What is probability?
    • Combining probabilities
    • The mean, variance, and standard deviation
    • Continuous probability distributions
  • Wave-particle duality
    • Introduction
    • Classical light-waves
    • The 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
  • Fundamentals of quantum mechanics
    • Introduction
    • Schrödinger's equation
    • Normalization of the wave-function
    • Expectation values and variances
    • Ehrenfest's theorem
    • Operators
    • The momentum representation
    • The uncertainty principle
    • Eigenstates and eigenvalues
    • Measurement
    • Continuous eigenvalues
    • Stationary states
  • One-dimensional potentials
    • Introduction
    • The infinite potential well
    • The square potential barrier
    • The WKB approximation
    • Cold emission
    • $\alpha$-decay
    • The square potential well
    • The simple harmonic oscillator
  • Multi-particle systems
    • Introduction
    • Fundamental concepts
    • Non-interacting particles
    • Two-particle systems
    • Identical particles
  • Three-dimensional quantum mechanics
    • Introduction
    • Fundamental concepts
    • Particle in a box
    • Degenerate electron gases
    • White-dwarf stars
  • Orbital angular momentum
    • Introduction
    • Angular momentum operators
    • Representation of angular momentum
    • Eigenstates of angular momentum
    • Eigenvalues of $L_z$
    • Eigenvalues of $L^2$
    • Spherical harmonics
  • Central potentials
    • Introduction
    • Derivation of radial equation
    • The infinite potential well
    • The hydrogen atom
    • The Rydberg formula
  • Spin angular momentum
    • Introduction
    • Spin operators
    • Spin space
    • Eigenstates of $S_z$ and $S^2$
    • The Pauli representation
    • Spin precession
  • Addition of angular momentum
    • Introduction
    • General principles
    • Angular momentum in the hydrogen atom
    • Two spin one-half particles
  
  
• Applications
  • Time-independent perturbation theory
    • Introduction
    • Improved notation
    • The two-state system
    • Non-degenerate perturbation theory
    • The quadratic Stark effect
    • Degenerate perturbation theory
    • The linear Stark effect
    • The fine structure of hydrogen
    • The Zeeman effect
    • Hyperfine structure
  • Time-dependent perturbation theory
    • Introduction
    • Preliminary analysis
    • The two-state system
    • Spin magnetic resonance
    • Perturbation expansion
    • Harmonic perturbations
    • Electromagnetic radiation
    • The electric dipole approximation
    • Spontaneous emission
    • Radiation from a harmonic oscillator
    • Selection rules
    • $2P\rightarrow 1S$ transitions in hydrogen
    • Intensity rules
    • Forbidden transitions
  • Variational methods
    • Introduction
    • The variational principle
    • The helium atom
    • The hydrogen molecule ion
  • Scattering theory
    • Introduction
    • Fundamentals
    • The Born approximation
    • Partial waves
    • Determination of phase-shifts
    • Hard sphere scattering
    • Low energy scattering
    • Resonances