Applications of non-orthogonal Laguerre function basis in helium atom

We present an L2 discretization of the helium atom using a non-orthogonal Laguerre function basis. The frozen-core approximation is used to calculate the helium atom Hamiltonian. The resulting three-term recurrence relation is a special case of the recurrence relation of the Pollaczek polynomials which is a set of orthogonal polynomials having a non-empty continuous spectrum in addition to an infinite discrete spectrum. The completeness of the helium atom wave functions obtained is studied in terms of weights of the Gauss quadrature.