  Most of the textbooks explaining electric conductivity in the context of
quantum mechanics provide either incomplete or semi-classical explanations that
are not connected with the elementary concepts of quantum mechanics. We
illustrate the conduction phenomena using the simplest model system in quantum
dynamics, a particle in a box (PIB). To induce the particle dynamics, a linear
potential tilting the bottom of the box is introduced, which is equivalent to
imposing a constant electric field for a charged particle. Although the PIB
model represents a closed system that cannot have a flow of electrons through
the system, we consider the oscillatory dynamics of the particle probability
density as the analogue of the electric current. Relating the amplitude and
other parameters of the particle oscillatory dynamics with the gap between the
ground and excited states of the PIB model allows us to demonstrate one of the
most basic dependencies of electric conductivity on the valence-conduction band
gap of the material.
