  Similarity Renormalization Group (SRG) flow equations can be used to
unitarily soften nuclear Hamiltonians by decoupling high-energy intermediate
state contributions to low-energy observables while maintaining the natural
hierarchy of many-body forces. Analogous flow equations can be used to
consistently evolve operators so that observables are unchanged if no
approximations are made. The question in practice is whether the advantages of
a softer Hamiltonian and less correlated wave functions might be offset by
complications in approximating and applying other operators. Here we examine
the properties of SRG-evolved operators, focusing in this paper on applications
to the deuteron but leading toward methods for few-body systems. We find the
advantageous features generally carry over to other operators with additional
simplifications in some cases from factorization of the unitary transformation
operator.
