Bethe believed that the atomic nucleus was like a quantum liquid drop. He investigated the nuclear matter problem by considering the work conducted by Keith Brueckner on perturbation theory. Working with Jeffrey Goldstone, he produced a solution for the case where there was an infinite hard-core potential. Then, working with Baird Brandow and Albert Petschek, he came up with an approximation that converted the scattering equation into an easily solved differential equation. This then led him to the Bethe-Faddeev equation, a generalisation of Ludvig Faddeev 's approach to three-body scattering. He then used these techniques to examine the neutron stars, which have densities similar to those of nuclei.