Rigorous mathematical study of the He bound statesстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:A method is proposed for searching the formal solution of the Hylleraas equation for the helium atom. A mathematically rigorous study confirms, in a unified and simpler manner, several results obtained earlier in the literature but not necessarily in the same contexts; We use an adequate transformation of the Schrodinger equation to identify three asymptotic channels. Two of these are considered in detail as physical and are seen to differ from "traditional" ones. In particular, we demonstrate that there is no place for the widely used Hylleraas-type exponent. Furthermore, we show how the mathematical presence of logarithms at small hyperradii, first suggested by Bartlett, is linked to the electron-electron interaction. Finally, the study leads to the development of simple procedures for the numerical calculations of energy levels and approximate wave functions.