  We show that the finite lateral sizes of ultrathin CdSe nanoplatelets
strongly affect both their photoluminescence and optical absorption spectra.
This is in contrast to the situation in quantum wells, in which the large
lateral sizes may be assumed to be infinite. The lateral sizes of the
nanoplatelets are varied over a range of a few to tens of nanometers. For these
sizes excitons experience in-plane quantum confinement, and their
center-of-mass motion becomes quantized. Our direct experimental observation of
the discretization of the exciton center-of-mass states can be well understood
on the basis of the simple particle-in-a-box model.
