A comparative study of two lattice approaches to two-body systems

We present a method to extract the spectrum of two-particle systems on the lattice from wave functions computed in lattice simulations. The energies of the Hamiltonian eigenstates are extracted from the eigenvalues of a matrix, similar to a potential, constrained by the wave functions. This method is compared with the traditional variational method in the isospin 2 $\pi \pi$ system.