We derive the corresponding conservation equation by integrating the Wigner equation over all velocities

(8.6) |

By definition the Wigner potential is an odd function in . Hence the contribution from the integral

vanishes. This property expresses conservation of particle number from potential scattering. In a similar way the term stemming from scattering also vanishes as we have

With the introduction of the (particle) current density :

(8.8) |

we finally get the continuity equation (in vector notation):

The aim is to find a discretization of the full Wigner equation which conserves mass.

** Previous:** 8.3 Conservation of Mass
**Up:** 8.3 Conservation of Mass
** Next:** 8.3.2 Meshing Constraints

R. Kosik: Numerical Challenges on the Road to NanoTCAD