  We study maps preserving the Heisenberg commutation relation $ab - ba=1$. We
find a one-parameter deformation of the standard realization of the above
algebra in terms of a coordinate and its dual derivative. It involves a
non-local ``coordinate'' operator while the dual ``derivative'' is just the
Jackson finite-difference operator. Substitution of this realization into any
differential operator involving $x$ and $\frac{d}{dx}$, results in an {\em
isospectral} deformation of a continuous differential operator into a
finite-difference one. We extend our results to the deformed Heisenberg algebra
$ab-qba=1$. As an example of potential applications, various deformations of
the Hahn polynomials are briefly discussed.
