  We investigate the transmission properties of a quantum one-dimensional
periodic system of fixed length $L$, with $N$ barriers of constant height $V$
and width $\lambda$, and $N$ wells of width $\delta$. In particular, we study
the behaviour of the transmission coefficient in the limit $N\to \infty$, with
$L$ fixed. This is achieved by letting $\delta$ and $\lambda$ both scale as
$1/N$, in such a way that their ratio $\gamma= \lambda/\delta$ is a fixed
parameter characterizing the model. In this continuum limit the multi-barrier
system behaves as it were constituted by a unique barrier of constant height
$E_o=(\gamma V)/(1+\gamma)$. The analysis of the dispersion relation of the
model shows the presence of forbidden energy bands at any finite $N$.
