  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.
