We start by following the treatment for coherent DNP described in . We consider a system consisting of a single S = 1/2 electron spin interacting with a single I=1/2 nuclear spin in the presence of a static magnetic and a microwave field. Per usual, we choose the z-axis of the laboratory frame of reference along the static magnetic field and the x-axis along the microwave field. In a frame rotating with the microwave frequency ωm about the z-axis and with ℏ = 1 the truncated spin Hamiltonian is then