  We explain recent experimental results on the superconducting state spectral
function as obtained by angle resolved photoemission, as well as by tunneling,
in high Tc cuprates. In our model, electrons are coupled to the resonant spin
fluctuation mode observed in inelastic neutron scattering experiments, as well
as to a gapped continuum. We show that, although the weight of the resonance is
small, its effect on the electron self energy is large, and can explain various
dispersion anomalies seen in the data. In agreement with experiment, we find
that these effects are a strong function of doping. We contrast our results to
those expected for electrons coupled to phonons.
