  We construct the string states $|O_{p}^J>_J$, $|O_{q}^{J_1}>_{{J_1}{J_2}}$
and $|O_{0}^{J_{1}J_{2}}>_{{J_1}{J_2}}$ in the Hilbert space of the quantum
mechanical orbifold model so as to calculate the three point functions and the
matrix elements of the light-cone Hamiltonian from the interacting string bit
model. With these string states we show that the three point functions and the
matrix elements of the Hamiltonian derived from the interacting string bit
model up to $g^{2}_2$ order precisely match with those computed from the
perturbative SYM theory in BMN limit.
