An orthonormal regularized Lagrange mesh for bound and scattering states

A regularized Lagrange mesh based on exactly orthonormal Lagrange-Laguerre functions is devised and applied to the study of bound states for two solvable radial potentials: the harmonic-oscillator and Coulomb potentials. The analysis of these results and a comparison with calculations based on other Lagrange meshes provide an explanation on the low accuracy of some Lagrange-mesh calculations in the presence of singularities in the potential. Although based on square-integrable functions, this Lagrange mesh can also be used for studying the elastic scattering, by means of integral relations. This approach is tested on two typical examples. Very accurate results are obtained with small numbers of mesh points.