In the general case, the difficult step of the transformation is to find an explicit expression for the generator S . Once this is done, it is straightforward to compute the Schrieffer-Wolff Hamiltonian by computing the commutator [ S , V ] . The Hamiltonian can then be projected on any subspace of interest to obtain an effective projected Hamiltonian for that subspace. In order for the transformation to be accurate, the eliminated subspaces must be energetically well separated from the subspace of interest, meaning that the strength of the interaction V must be much smaller than the energy difference between the subspaces. This is the same regime of validity as in standard second-order perturbation theory.