  We derive an analytical expression for the intermediate scattering function
of a particle on a flat surface obeying the Generalised Langevin Equation, with
exponential memory friction. Numerical simulations based on an extended phase
space method confirm the analytical results. The simulated trajectories provide
qualitative insight into the effect that introducing a finite memory timescale
has on the analytical line shapes. The relative amplitude of the long-time
exponential tail of the line shape is suppressed, but its decay rate is
unchanged, reflecting the fact that the cutoff frequency of the exponential
kernel affects short-time correlations but not the diffusion coefficient which
is defined in terms of a long-time limit. The exponential sensitivity of the
relative amplitudes to the decay time of the chosen memory kernel is a very
strong indicator for the prospect of inferring a friction kernel and the
physical insights from experimentally measured intermediate scattering
functions.
