Laguerre meshes in atomic structure calculations

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Abstract
A new method to discretise the Schrodinger equations has been described recently and applied successfully to simple quantum mechanical and nuclear Hartree-Fock problems. The method is based on an accurate approximation of a variational calculation. The authors apply this approach in atomic structure calculations by discretising on Laguerre meshes the Schrodinger equation for hydrogen and the Hartree-Fock and configuration interaction equations of two-electron systems. They investigate the accuracy of the method for the ground states and some of the excited states of H, He and H-. They illustrate the striking simplicity of the Hamiltonian matrix elements arising from the Lagrange functions properties when using the Gauss quadrature integration formula and test its accuracy as a function of the number of points defining the mesh. They also test the quality of the Lagrange function basis set by checking sum rules and by calculating the second-order energy of helium.