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Chapter 2
Wigner Formalism of Quantum Mechanics

This chapter first discusses the Wigner transport equation and its derivation. Thereafter, the addition of scattering models to the Wigner equation is discussed, which leads to the Wigner-Boltzmann equation (WBE). The semi-discrete form of the Wigner equation is then presented. Finally, an overview of the existing solvers for the WBE is given.

 2.1 Wigner equation
  2.1.1 History and derivation
  2.1.2 Properties
 2.2 Wigner-Boltzmann equation
  2.2.1 Derivation
 2.3 Discretization of momentum space
  2.3.1 Semi-discrete Wigner equation
 2.4 Transport problems
  2.4.1 Boundary and initial conditions
  2.4.2 Stationary
  2.4.3 Transient
 2.5 Overview of existing solvers
  2.5.1 Deterministic methods
  2.5.2 Stochastic methods

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