  The current paper is devoted to the scattering theory of a class of continuum
Schr\"{o}dinger operators with deterministic sparse potentials. We first
establish the limiting absorption principle for both modified free resolvents
and modified perturbed resolvents. This actually is a weak form of the
classical limiting absorption principle. We then prove the existence and
completeness of local wave operators, which, in particular, imply the existence
of wave operators. Under additional assumptions on the sparse potential, we
prove the completeness of wave operators. In the context of continuum
Schr\"{o}dinger operators with sparse potentials, this paper gives the first
proof of the completeness of wave operators.
