The nucleon-nucleon interaction is one of the most complicated occurring in quantum mechanics -- on fundamental grounds it contains spin-spin, tensor, L.S, and isospin dependencies; to fit the scattering data additional terms involving second derivatives of positions must also be included. Furthermore accurate models of nuclei must also consider three-nucleon potentials with similar terms. Reliable many-body calculations with such a Hamiltonian are very difficult; through the 1980's only the two- and three-nucleon problems were accurately solved. Variational Monte Carlo (VMC) calculations have been made for many years for light nuclei, but their accuracy was never established. In the last decade Green's function Monte Carlo (GFMC) was used for 4He and, more recently, for 6- to 8-nucleon systems. These calculations in fact show that the VMC wave functions are not adequate for p-shell nuclei.

In these lectures I will describe the VMC and GFMC methods as applied to nuclei. I will spend some of the time on the computational details and use of parallel computers for these massive calculations. Finally I will present results and comment on our knowledge of the nuclear Hamiltonian.