A relatively simple many-electron basis is used to construct a matrix for the Anderson impurity Hamiltonian. The basis states are each valid in the thermodynamic limit. The approximate ground-state energy compares well with Bethe-ansatz results for large Coulomb energies. The ground-state wave-function properties are not as well approximated. This method may be well suited to studies of more realistic Hamiltonians and their ground-state energy and its derivatives.