  In this paper, a link between $q$-difference equations, Jacobi operators and
orthogonal polynomials is given. Replacing the variable $x$ by $ q^{-n}$ in a
Sturm-Liouville $q$-difference equation we discovered the Jacobi operator. With
appropriate initial conditions, the eigenfunctions of such operators are either
$q$-orthogonal polynomials or the modified $q$-Bessel function and a newborn
the $q$-Macdonald ones. The new Polynomial sequence we found is related to the
$q$-Lommel polynomials introduced by Koelink and other. Adapting E. C.
Titchmarsh's theory, we showed the existence of a solution square-integrable
only in the complex case. As application in the real case we gave the behavior
at infinity for $q$-Macdonald's function. Finally, we pointed out that the
method described in our paper can be generalized to study the orthogonal
polynomial sequence introduced by Al-Salam and Ismail
