Electrons occupying surface states on the close-packed faces of the no
ble metals form a two-dimensional (2D) electron gas that is accessible
to the scanning tunneling microscope (STM), Using a cryogenic STM, we
have observed quantum mechanical interference patterns arising from 2
D electrons on the surface of Cu. These interference patterns can be a
rtificially controlled by arranging individual Fe atoms into ''quantum
corrals'' on the Cu surface, Quantum corrals behave qualitatively lik
e 2D hard-wall boxes, but a quantitative understanding is obtained wit
hin a multiple scattering formalism. The scattering here is characteri
zed by a complex phase shift which can be extracted from the electroni
c density pattern near a quantum corral.