  The energy of a quantum particle cannot be determined exactly unless there is
an infinite amount of time in which to perform the measurement. This paper
considers the possibility that $\Delta E$, the uncertainty in the energy, may
be complex. To understand the effect of a particle having a complex energy, the
behavior of a classical particle in a one-dimensional periodic potential
$V(x)=-\cos(x)$ is studied. On the basis of detailed numerical simulations it
is shown that if the energy of such a particle is allowed to be complex, the
classical motion of the particle can exhibit two qualitatively different
behaviors: (i) The particle may hop from classically-allowed site to
nearest-neighbor classically-allowed site in the potential, behaving as if it
were a quantum particle in an energy gap and undergoing repeated tunneling
processes, or (ii) the particle may behave as a quantum particle in a
conduction band and drift at a constant average velocity through the potential
as if it were undergoing resonant tunneling. The classical conduction bands for
this potential are determined numerically with high precision.
