  In this article, we investigate the semiclassical version of the wave
equation for the discrete Schr\"{o}dinger operator,
$\mathcal{H}_{\hbar,V}:=-\hbar^{-2}\mathcal{L}_{\hbar}+V$ on the lattice
$\hbar\mathbb{Z}^{n},$ where $\mathcal{L}_{\hbar}$ is the discrete Laplacian,
and $V$ is a non-negative multiplication operator. We prove that
$\mathcal{H}_{\hbar,V}$ has a purely discrete spectrum when the potential $V$
satisfies the condition $|V(k)|\to \infty$ as $|k|\to\infty$. We also show that
the Cauchy problem with regular coefficients is well-posed in the associated
Sobolev type spaces and very weakly well-posed for distributional coefficients.
Finally, we recover the classical solution as well as the very weak solution in
certain Sobolev type spaces as the limit of the semiclassical parameter
$\hbar\to 0$.
