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7.2.6 Scattering in the QTBM

With the electron-phonon scattering operator
given in (classical) phase space scattering is described
by Fermi's golden rule.
In Chapter 9 we will include this classical description
for scattering in the quantum Wigner Equation 8.1
to solve this model by Monte Carlo methods.

The fundamental reason, why this model cannot be adequately
formulated within the QTBM,
is that the corresponding equation
for the density matrix cannot be separated, that is, there
is no corresponding single particle Schrödinger equation.
This model can only be formulated with the use of densities.

What we need technically is a method to describe a single
particle (wave function, pure state) in contact with
a phonon bath (density, mixed state) within the QTBM.
Formulation of such
models for scattering is the topic
of the next subsections.

**Subsections**
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R. Kosik: Numerical Challenges on the Road to NanoTCAD