dorsal/arxiv
View SchemaExperiment and Theory in Computations of the He Atom Ground State
| Authors | Charles Schwartz |
|---|---|
| Categories | |
| ArXiv ID | physics/0208004 |
| URL | https://arxiv.org/abs/physics/0208004 |
| DOI | 10.1142/S0218301306004648 |
| Journal | Int. J. Mod. Phys. E15, 877 (2006) |
Abstract
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.
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"abstract": "Extensive variational computations are reported for the ground state energy\nof the non-relativistic two-electron atom. Several different sets of basis\nfunctions were systematically explored, starting with the original scheme of\nHylleraas. The most rapid convergence is found with a combination of negative\npowers and a logarithm of the coordinate s = r_{1}+ r_{2}. At N=3091 terms we\npass the previous best calculation (Korobov\u0027s 25 decimal accuracy with N=5200\nterms) and we stop at N=10257 with E = -2.90372 43770 34119 59831 11592 45194\n40444 ...\n Previous mathematical analysis sought to link the convergence rate of such\ncalculations to specific analytic properties of the functions involved. The\napplication of that theory to this new experimental data leaves a rather\nfrustrating situation, where we seem able to do little more than invoke vague\nconcepts, such as ``flexibility.\u0027\u0027 We conclude that theoretical understanding\nhere lags well behind the power of available computing machinery.",
"arxiv_id": "physics/0208004",
"authors": [
"Charles Schwartz"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1142/S0218301306004648",
"journal_ref": "Int. J. Mod. Phys. E15, 877 (2006)",
"title": "Experiment and Theory in Computations of the He Atom Ground State",
"url": "https://arxiv.org/abs/physics/0208004"
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