  After removing the double-well potential trapping two initially independent
Bose condensates, the density expectation value is calculated when both the
exchange symmetry of identical bosons and interatomic interaction are
considered. After the overlapping, it is shown that there is a nonzero
interference term in the density expectation value. This nonzero interference
term physically arises from the exchange symmetry of identical bosons and
interatomic interaction which make two initially independent condensates become
coherent after the overlapping. It is found that the calculated density
expectation value with this model agrees with the interference pattern observed
in the experiment by Andrews et al (Science 275, 637 (1997)).
