 Let Ω be an ordering of the non-commutative creation and annihilation operators, and let formula_1 be an operator that is expressible as a power series in the creation and annihilation operators that satisfies the ordering Ω.Then the optical equivalence theorem is succinctly expressed as

Here, is understood to be the eigenvalue of the annihilation operator on a coherent state and is replaced formally in the power series expansion of .The left side of the above equation is an expectation value in the Hilbert space whereas the right hand side is an expectation value with respect to the quasiprobability distribution.