2002/08/01 by Charles Schwartz · 1 citation
Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Quantum Mechanics and Non-Hermitian Physics #physics.atom-ph
paper · pdf · doi:10.1142/s0218301306004648
published as Int. J. Mod. Phys. E15, 877 (2006) · 15 pages
arxiv created 2002/08/01 · openalex publication_date 2006/04/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Extensive variational computations are reported for the ground state energy of the non-relativistic two-electron atom. Several different sets of basis functions were systematically explored, starting with the original scheme of Hylleraas. The most rapid convergence is found with a combination of negative powers and a logarithm of the coordinate s = r 1 + r 2 . At N = 3091 terms we pass the previous best calculation (Korobov's 25 decimal accuracy with N = 5200 terms) and we stop at N = 10257 with E = -2.90372, 43770, 34119, 59831, 11592, 45194, 40444, …. Previous mathematical analysis sought to link the convergence rate of such calculations to specific analytic properties of the functions involved. The application of that theory to this new experimental data leaves a rather frustrating situation, where we seem able to do little more than invoke vague concepts, such as "flexibility." We conclude that theoretical understanding here lags well behind the power of available computing machinery.