New method for merging several exponential operators’ product into one exponential operator

For two operators [Formula: see text] and [Formula: see text] which obey [Formula: see text]we shall prove [Formula: see text]which means we want to merge two exponential operators’ product into one exponential operator. This kind of operator identity is useful for calculating the quantum entropy [Formula: see text] since [Formula: see text] when [Formula: see text] but [Formula: see text] thus the merging operator formula is demanded. In this way, several exponential operators’ product can also be merged. We shall employ the method of integration within normally ordered product (IWOP) to derive the merging operator identity.