The fixed hypernode method for the solution of the many body schroedinger equation

We propose a new scheme for an approximate solution of the Schroedinger equation for a many-body interacting system, based on the use of pairs of walkers. Trial wavefunctions for these pairs are combinations of standard symmetric and antisymmetric wavefunctions. The method consists in applying a fixed-node restriction in the enlarged space, and computing the energy of the antisymmetric state from the knowledge of the exact ground state energy for the symmetric state. We made two conjectures: first, that this fixed-hypernode energy is an upper bound to the true fermion energy; second, that this bound is lower than the usual fixed-node energy using the same antisymmetric trial function. The first conjecture is true, and is proved in this paper. The second is not, and numerical and analytical counterexamples are given. The question of whether the fixed-hypernode energy can be better than the usual bound remains open.