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In this chapter we study the orthodox formulation
of quantum (wave) mechanics using the Schrödinger
and the von Neumann equation. First we study
single particle transport as described by the Schrödinger
equation with absorbing boundary conditions.
Then we solve the open boundary von Neumann equation
by reducing it to a set of Schrödinger equations
using the separation ansatz.
This is known as the quantum transmitting boundary method
(QTBM).
Finally we discuss the modeling of scattering using
hydrodynamical variables within the QTBM.

**Subsections**
** Previous:** 6.2.7 Quantum Propagators and
**Up:** III. Quantum Simulation of
** Next:** 7.1 Single Particle Transport

R. Kosik: Numerical Challenges on the Road to NanoTCAD