  We investigate the evolution of an electron undergoing coherent tunneling via
adiabatic passage (CTAP) using the solution of the one-dimensional Schroedinger
equation in both space and time for a triple well potential. We find the
eigenspectrum and complete time evolution for a range of different pulsing
schemes. This also provides an example of a system that can be described with
the tools from both quantum optics and condensed matter. We find that while the
quantum optics description of the process captures most of the key physics,
there are important effects that can only be correctly described by a more
complete representation. This is an important point for applications such as
quantum information processing or quantum control where it is common practice
to use a reduced state space formulation of the quantum system in question.
