The non-uniqueness of solutions of the nonlinear integral equations for the generalized Chandrasekhar′s function and H matrix for a homogeneous halfspace is discussed, and a new uniquely soluble equation for the H matrix is constructed. Then the complete solutions for the half-space albedo and Milne problems for thermal neutrons with the isotropic scattering degenerate kernel are derived. The solutions are expanded in terms of the infinite medium eigenfunctions and the expansion coefficients are determined from the corresponding emergent distributions, which have been discussed in an earlier paper and expressed in terms of the H matrix. In solving the albedo problem, the half-range completeness of the eigenfunctions is demonstrated and the corresponding halfrange closure relation is derived. At the end, numerical results for the heavy gas scattering model are presented.