We　propose　a　scheme　to　drive　the　vibrational　motion　of　a　trapped　ion　to　an　arbitrary　quantum　state　from　the　vacuum　state.　In　the　scheme　the　ion　is　excited　by　a　sequence　of　laser　pulses　tuned　to　the　respective　lower　vibrational　sidebands.　Finally,　the　system　evolves　into　a　pure　state　given　by　the　product　of　the　ground　electronic　state　with　the　desired　vibrational　state.　(C)　1998　Elsevier　Science　B.V.