The ground‐state energy of a spin‐density wave of wave vector Q in a Heisenberg ferromagnet with competing interactions is calculated for small Q as E G (Q)=E G (0)+A 1 Q 2 +A 2 Q 4+ . . . . The coefficients A 1 and A 2 are calculated exactly at zero temperature in the limit as the ferromagnet to helix transition is approached. For some ranges of parameters we find that quantum zero point motion causes A 2 to become negative thus leading to a first‐order transition not present in the classical system.