  Carbon nanotubes provide a unique system to study one-dimensional
quantization phenomena. Scanning tunneling microscopy is used to observe the
electronic wave functions that correspond to quantized energy levels in short
metallic carbon nanotubes. Discrete electron waves are apparent from periodic
oscillations in the differential conductance as a function of the position
along the tube axis, with a period that differs from that of the atomic
lattice. Wave functions can be observed for several electron states at adjacent
discrete energies. The measured wavelengths are in good agreement with the
calculated Fermi wavelength for armchair nanotubes.
