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A very accurate grid method for the solution of Schrödinger equations: The helium ground state
Author(s) -
Newman F. T.
Publication year - 1997
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1997)63:6<1065::aid-qua1>3.0.co;2-v
Subject(s) - superconvergence , helium , extrapolation , ground state , eigenvalues and eigenvectors , schrödinger equation , physics , electron , grid , mathematics , quantum mechanics , atomic physics , mathematical analysis , geometry , finite element method , thermodynamics
An extension to the theory of Schrödinger equations has beenmade which enables the derivation of eigenvalues from a consideration of avery small part of geometric space. The concomitant unwanted continuumeffects have been removed. The theory enables very convergent or“superconvergent” calculations. In the case of the heliumground state, E =−2.90372437703411987 E h was obtained from 251 terms. The result iscomparable to that from the largest variation calculations so far carriedout reinforced by extrapolation techniques. The theory is extensible toatoms and molecules irrespectively of the number of electrons or nuclearcenters. In these cases, the advantage of “superconvergent”calculations will be more pronounced than in the case ofhelium. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63 : 1065–1078, 1997