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On the analytic solution of the first‐order perturbed wave function of the two‐electron atom
Author(s) -
White Ronald J.,
Brown W. Byers
Publication year - 2009
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/qua.560010606
Subject(s) - power series , helium atom , perturbation (astronomy) , wave function , ground state , atom (system on chip) , recursion (computer science) , mathematics , differential equation , electron , first order , mathematical analysis , physics , quantum mechanics , algorithm , computer science , embedded system
It is shown that the first‐order perturbation equation for the ground state of the helium atom, with r −1 12 as the perturbation, may be solved by an infinite power series in r 12 . The coefficients, which are functions of r 1 and r 2 , satisfy two‐term differential recursion relations which can be integrated analytically to give the higher coefficients in terms of the lower. In this preliminary communication, the first coefficient, which describes short‐range correlation, is given explicitly. The extensions of the technique are discussed.