  In this paper we consider the semiclassical version of pseudo-differential
operators on the lattice space $\hbar \mathbb{Z}^n$. The current work is an
extension of a previous work and agrees with it in the limit of the parameter
$\hbar \rightarrow 1$. The various representations of the operators will be
studied as well as the composition, transpose, adjoint and the link between
ellipticity and parametrix of operators. We also give the conditions for the
$\ell^p(\hbar \mathbb{Z}^n)$, weighted $\ell^2(\hbar \mathbb{Z}^n)$ boundedness
and $\ell^p(\hbar \mathbb{Z}^n)$ compactness of operators. We investigate the
relation between the classical and semi-classical quantization and employ its
applications to Schatten-Von Neumann classes on $\ell^2( \hbar \mathbb{Z}^n)$.
We establish G\r{a}rding and sharp G\r{a}rding inequalities, with an
application to the well-posedness of parabolic equations on the lattice $\hbar
\mathbb{Z}^n$. Finally we verify that in the limiting case where $\hbar
\rightarrow 0$ the semi-classical calculus of pseudo-differential operators
recovers the classical Euclidean calculus, but with a twist.
