1 Introduction
2 Basics of Quantum Cascade Lasers
 2.1 Fundamentals
 2.2 Milestones and State-of-the-art
 2.3 Applications
3 Quantum Ballistic Transport
 3.1 The Effective Mass Approximation
 3.2 Schrödinger-Poisson Solver
 3.3 Boundary Conditions
  3.3.1 Dirichlet and Neumann Boundary Conditions
  3.3.2 Open Boundary Conditions
   3.3.2.1 Asymptotic Behavior
 3.4 Non-Equilibrium Green’s Functions
4 Quantum Dissipative Transport
 4.1 Density Matrix Formulation
  4.1.1 Density Matrix Equations for Dissipative Systems
   4.1.1.1 Markov Approximation
   4.1.1.2 The Relaxation Equation
   4.1.1.3 From the Liouville-von Neumann Equation to the PME
 4.2 Semiclassical Transport Description
  4.2.1 Pauli Master Equation
  4.2.2 Monte Carlo Method
5 Scattering Rates
 5.1 Phonons
 5.2 From Fermi’s Golden Rule to the Totel Scattering Rate
 5.3 Polar Optical Phonon Scattering
 5.4 Acoustic Deformation Potential Scattering
 5.5 Optical Deformation Potential Scattering
 5.6 Intervalley Scattering
 5.7 Interface Roughness Scattering
 5.8 Alloy Scattering
6 Simulation Results
 6.1 Quantum Ballistic Transport Calculations
  6.1.1 Tunneling Current Density
   6.1.1.1 Comparison with the Tsu-Esaki Model
   6.1.1.2 Comparison with the NEGF Approach
  6.1.2 Optical Gain
   6.1.2.1 Calculation Results
 6.2 Design and Perfomance Investigations
  6.2.1 A THz QCL
   6.2.1.1 Structure
   6.2.1.2 Results
   6.2.1.3 Interface Roughness Effects
  6.2.2 Mid-infrared QCL
   6.2.2.1 Initial Structure
   6.2.2.2 Optimization of the Collector Barrier
  6.2.3 Simulation of an Al-free QCL
   6.2.3.1 Structure
   6.2.3.2 Results of the Monte Carlo Simulation
   6.2.3.3 Inclusion of Alloy Scattering
7 Summary and Outlook