  The local density of states \rho(x,E) is calculated for a Bloch electron in
an electric field. Depending on the system size, we can see one or more
sequences of Wannier-Stark ladders in \rho(x,E), with Lorentz type level widths
and apparent spatial localization of the states. Our model is a chain of delta
function potential barriers plus a step-like electric potential, with open
boundary condition at both ends of the system. Using a wave tunneling picture,
we find that the level widths shrink to zero as an inverse power as the system
size approaches infinity, confirming an earlier result.
