STANDING-WAVE patterns in electron density have been seen recently(1-4
) in images of the surfaces of noble metals obtained with the scanning
tunnelling microscope (STM). These patterns are due to the scattering
of surface electrons off impurities and step edges. By assembling spe
cific enclosed structures of adatoms ('quantum corrals') using the STM
, one can generate standing waves of particular geometries(3). Here we
describe a theory of the scattering process, which allows us to predi
ct the standing-wave patterns of an arbitrary corral geometry with gre
at accuracy. We can use the theory to examine the scattering propertie
s of the atoms in the corral walls. We find that iron atoms assembled
on the (111) surface of copper act as 'black dots', soaking up all of
the electron wave amplitude impinging on them. A scattered wave is gen
erated nonetheless, but this behaviour means that the corral walls are
only 25% reflective. In an acoustic analogy, the corral is therefore
a rather quiet chamber.