The solution of the Schrödinger equation in imaginary time by Green’s function Monte Carlo. The rigorous sampling of the attractive Coulomb singularity

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Abstract
We present a new Green’s function Monte Carlo method for solving for the ground state of the Schrödinger equation. Unlike the commonly used short time approximation this method has no time step error. We formulate the method so that the attractive Coulomb singularities are isolated and can be accurately sampled. The algorithm is used to obtain the ground state energies of the following atomic systems: H, He and the helium-like ions of Be, N, and O. The results compare favorably with the experimental ground state energies.