  We investigate the dynamics of a tagged particle embedded in a strongly
interacting confined liquid enclosed between two opposing flat walls. Using the
Zwanzig-Mori projection operator formalism we obtain an equation of motion for
the incoherent scattering function suitably generalized to account for the lack
of translational symmetry. We close the equations of motion by a
self-consistent mode-coupling ansatz. The interaction of the tracer with the
surrounding liquid is encoded in generalized direct correlation functions. We
extract the in-plane dynamics and provide a microscopic expression for the
diffusion coefficient parallel to the walls. The solute particle may differ in
size or interaction from the surrounding host-liquid constituents offering the
possibility of a systematic analysis of dynamic effects on the tagged-particle
motion in confinement.
