  The Diffusion Monte Carlo method is devoted to the computation of electronic
ground-state energies of molecules. In this paper, we focus on implementations
of this method which consist in exploring the configuration space with a {\bf
fixed} number of random walkers evolving according to a Stochastic Differential
Equation discretized in time. We allow stochastic reconfigurations of the
walkers to reduce the discrepancy between the weights that they carry. On a
simple one-dimensional example, we prove the convergence of the method for a
fixed number of reconfigurations when the number of walkers tends to $+\infty$
while the timestep tends to 0. We confirm our theoretical rates of convergence
by numerical experiments. Various resampling algorithms are investigated, both
theoretically and numerically
