  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. The density expectation value and evolution equations are obtained
based on both the first-quantization and second-quantization methods. When the
interatomic interaction is considered carefully, after the overlapping of two
initially independent condensates, it is shown that there is a nonzero
interference term in the density expectation value. It is found that the
calculated density expectation value with this model agrees with the
interference pattern observed in the experiment by Andrews (Science 275, 637
(1997)). The nonzero interference term in the density expectation value
physically arises from the exchange symmetry of identical bosons and
interatomic interaction which make two initially independent condensates become
coherent after the overlapping. For two initially independent condensates, our
researches show that there is an interaction-induced coherence process.
