  The Wigner-Liouville equation is reformulated using a spectral decomposition
of the classical force field instead of the potential energy. The latter is
shown to simplify the Wigner-Liouville kernel both conceptually and numerically
as the spectral force Wigner-Liouville equation avoids the numerical evaluation
of the highly oscillatory Wigner kernel which is nonlocal in both position and
momentum. The quantum mechanical evolution is instead governed by a term local
in space and non-local in momentum, where the non-locality in momentum has only
a limited range. An interpretation of the time evolution in terms of two
processes is presented; a classical evolution under the influence of the
averaged driving field, and a probability-preserving quantum-mechanical
generation and annihilation term. Using the inherent stability and reduced
complexity, a direct deterministic numerical implementation using Chebyshev and
Fourier pseudo-spectral methods is detailed. For the purpose of illustration,
we present results for the time-evolution of a one-dimensional resonant
tunneling diode driven out of equilibrium.
