A new theoretical method for describing QCLs is presented. The method extends the familiar incoherent rate equations to include
coherence. Smooth output power and voltage curves as function of current are obtained at very modest computational effort.
Coherence is shown to play an important role in QCLs. The method is derived by imposing the following requirements on the
equations of motion of the density matrix: 1. Expectation values should be independent of the choice of basis; 2. The density matrix
should be positive definite; 3. The model should reduce to existing rate-equation models when coherences are omitted.