Gyanendra P Sasmal 2009 J. Phys. B: At. Mol. Opt. Phys. 42 225001 doi:10.1088/0953-4075/42/22/225001
Gyanendra P Sasmal
Show affiliationsA three-dimensional finite volume discretization of the time-independent Schrödinger equation is formulated for the ground state helium atom. A set of algebraic equations arising from the second-order discretization of the PDE are solved for the wavefunction using the Gauss–Seidel algebraic multigrid solver coupled with a modified Stodola–Vianello method in extracting the ground state energy. A thorough mesh refinement study results in the ground state energy of the helium atom to be −2.903 230 au, which is only 0.017% above the Frankowski–Pekeris value. Mesh convergence of the wavefunction solution suggests that it correctly approximates to the unknown exact solution.
31.15.-p Calculations and mathematical techniques in atomic and molecular physics
Issue 22 (28 November 2009)
Received 17 July 2009, in final form 30 September 2009
Published 30 October 2009
Gyanendra P Sasmal 2009 J. Phys. B: At. Mol. Opt. Phys. 42 225001
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