Quantum mechanical ground states, nonlinear Schrodinger equations and linked cluster expansions

The ground state wavefunction of an infinitely large, spatially homogeneous system is evaluated in terms of wavefunctions for linked clusters of points within the system. The linked cluster wavefunction is shown to obey a nonlinear form of the Schrodinger equation, with the unlinked pieces providing the nonlinearity. A variational principle for the ground state energy is derived.