Convergent Energy States and Wave Functions of Helium Atom in an L2 Basis

Abstract

The convergence of energy states and wave functions of helium atom is presented. The energy states are obtained by diagonalizing the helium Hamiltonian in a non-orthogonal Laguerre basis. Some of the energy states will be exact discrete eigenstates, others will be a discrete representation of the continuum states. As the basis size N increases the lowest bound states in energy states converge to the exact eigenstates, whereas the positive energy states provide an increasingly dense discretization of the continuum. The convergence of wave functions is obtained by the Gauss-Pollaczek quadrature method.