Elementary Excitations in Trapped BEC and Zero Mode Problem
  We propose a natural expansion of the atomic field operator in studying elementary excitations in trapped Bose-Einstein Condensation (BEC) system near T=0K. Based on this expansion, a system of coupled equations for elementary excitations, which is equivalent to the standard linearized GP equation, is given to describe the collective excitation of BEC in a natual way. Applications of the new formalism to the homogeneous case emphasize on the zero mode and its relevant ground state of BEC. 
D.L.Zhou, X.X.Yi, G.R.Jin, Y.H.Su, Y.X.Liu, C.P.Sun