Contents

• The Radiation Laws and the Birth of Quantum Mechanics
  • Kirchhoff (5 min)
  • Rayleigh-Jeans law (5 min)
  • * Planck's law (10 min)
  • ** Stefan-Boltzmann constant (20-60 min)
  
  
• Waves, particles, and wave packets
  • Macroscopic Object (5 min)
  • * Geometrical Optic (2 min)
  
  
• Interpretation of the Wave Function
  • Schrödinger Equation (5 min)
  • Interpretation of the Wave Function (2 min)
  • Probability (2 min)
  • Probability and current density of a particle (15 min)
  
  
• Fourier Transforms and the Solution of the Schrödinger Equation
  • Definition of the Fourier Integral (2 min)
  • ** Math: Gauß (20 min)
  • * Math: Gauß Integral 1 (10 min)
  • Math: Gauß Integral 2 (10 min)
  • Math: Fourier Transform of Gauss Function (20 min)
  • * Wave packet (20 min)
  
  
• Position and Momentum in Quantum Mechanics
  • Normalization (2min)
  • Expectation values in quantum mechanics (5min)
  • Wave packet (10-30 min)
  • * Hamilton function (10min)
  • * Commutator 1 (10 min)
  
  
• The stationary Schrödinger Equation
  • Definitions (2min)
  • Piecewise constant potentials in one dimension (5min)
  
  
• The Infinite Potential Well
  • Energies and Eigenstates I (10-20 min)
  • Energies and Eigenstates II (10-20 min)
  • * Orthonormality (10 min)
  • Time Evolution (2 min)
  • Expectation values (15 min)
  • * Time evolution of superposition (10 min)
  
  
• The Finite Potential Well
  • Parity (10 min)
  • Wave functions (5 min)
  
  
• Scattering states in one dimension
  • Plane Waves (5 min)
  • Piecewise constant potential (25 min)
  • Transfer matrix (5 min)
  • Transmission, * Reflection (10min)
  
  
• The Tunnel Effect and Scattering Resonances
  • -matrix for tunnel barrier (15 min)
  • * Transmission coefficient (15 min)
  • Transmission coefficient (10 min)
  • ** Determinant of (10 min)
  • ** A more general definition of the transfer matrix ( min)
  
  
• Axioms of Quantum Mechanics and the Hilbert Space
  • Definition (2min)
  • Orthonormality (5 min)
  • * Expansion into eigenmodes (40 min)
  • * Scalar product (20 min)
  
  
• Operators and Measurements in Quantum Mechanics
  • Definitions (2 min)
  • Adjoint operator (10 min)
  • Observables (5 min)
  • Eigenvalues (5min)
  
  
• The Two-Level System I
  • Model (20 min)
  • Eigenvalues of the energy, eigenvectors (50 min)
  • Absorption Experiment (5 min)
  • * Vector Representation (10 min)
  
  
• The Two-Level System: Measurements and Probabilities
  • Qubit 1 (5 min)
  • Qubit 2 (5 min)
  • Qubit 3: NOT-Gate (5 min)
  • * Qubit 4: HADAMARD-Gate (10 min)
  
  
• The Harmonic Oscillator
  • Model (2 min)
  • Energies (2 min)
  • Linear combination (10-20 min)
  • ** Generating Function (5-30 min)
  
  
• Ladder Operators and Phonons
  • Commutator (5 min)
  • Hamiltonian (10 min)
  • Ladder Operator (5 min)
  • Ladder Operator (15 min)
  • Ground state (20 min)
  
  
• Central Potentials in Three Dimensions
  • Separations of Variables (20 min)
  • * Behavior for und (10-20 min)
  
  
• About this document ...

The lecture homepage is http://brandes.phy.umist.ac.uk/QM/