  Electronic standing waves with two different wavelengths were directly mapped
near one end of a single-wall carbon nanotube as a function of the tip position
and the sample bias voltage with highresolution position-resolved scanning
tunneling spectroscopy. The observed two standing waves caused by separate spin
and charge bosonic excitations are found to constitute direct evidence for a
Luttinger liquid. The increased group velocity of the charge excitation, the
power-law decay of their amplitudes away from the scattering boundary, and the
suppression of the density of states near the Fermi level were also directly
observed or calculated from the two different standing waves.
