The hydrogen atom and the H+2 and HeH++ molecular ions inside prolate spheroidal boxes

We formulate the exact solution of the Schrödinger equation for systems of one electron in the Coulomb field of one or two fixed nuclei at the foci inside prolate spheroidal boxes. Numerical results are obtained for the energy eigenvalues and eigenfunctions of the lowest states of the hydrogen atom and the H+2 and HeH++ molecular ions for boxes of different sizes and eccentricities. We also evaluate the hyperfine splitting of atomic hydrogen and of H+2.