Aspects of Spin Dynamics in the Cuprate Superconductors

One of the interesting aspects of the CuO superconductors is that superconductivity is happening so close to the antiferromagnetic state. The nuclear magnetic resonance and the recent neutron scattering experiments clearly indicate that magnetic correlations persist in to the heavily doped regime. In this paper we will discuss some of the details of the coupling of the nuclear magnetic spin to the conduction electron spins. Furthermore we will show that a simple band structure can explain the recent neutron scattering data in the \LaSrCuO material for the optimal concentration of $x\approx 0.15$ if the lifetime effects are included.