The spectrum of resonance fluorescence of a single trapped and laser-c
ooled ion is studied theoretically. The quantum motion of the trapped
particle manifests itself in the form of narrow motional sidebands in
the fluorescence spectrum. For our calculations it is assumed that the
ion is confined to dimensions much smaller than the optical wavelengt
h (Lamb-Dicke limit) and the approach is valid for multilevel systems,
general trapping potentials, and for both traveling-wave and standing
-wave configurations. The motional sidebands in the spectrum have asym
metric amplitudes and this asymmetry is shown to depend on the ion ene
rgy, the detector position, and the choice of standing- or traveling-w
ave laser excitation.