Optical wavelet-fractional squeezing combinatorial transform

By virtue of the method of integration within ordered product (IWOP) of operators we find the normally ordered form of the optical wavelet-fractional squeezing combinatorial transform (WFrST) operator. The way we successfully combine them to realize the integration transform kernel of WFrST is making full use of the completeness relation of Dirac's ket-bra representation. The WFrST can play role in analyzing and recognizing quantum states, for instance, we apply this new transform to identify the vacuum state, the single-particle state, and their superposition state.