  A set of equations is derived from the Boltzmann kinetic equation describing
charge transport in semiconductors. The unknowns of these equations depend on
the space-time coordinates and the electron energy. The non-parabolic and
parabolic band approximation are treated in detail. In these cases, the set of
equations is equivalent to those obtained in the spherical-harmonics expansion.
Stationary and homogeneous solutions are explicitly treated. In order to solve
numerically the equations, a cut in the energy range is introduced. The
modified model maintains the physical characteristics of the original
equations. The solution of an asymptotic equation is found and compared to the
numerical solutions.
