Rigorous mathematical study of the He bound states - art. no. 042702

A method is proposed for searching the formal solution of the Hylleraas equ ation for the helium atom. A mathematically rigorous study confirms, in a u nified and simpler manner, several results obtained earlier in the literatu re but not necessarily in the same contexts; We use an adequate transformat ion 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 math ematical presence of logarithms at small hyperradii, first suggested by Bar tlett, is linked to the electron-electron interaction. Finally, the study l eads to the development of simple procedures for the numerical calculations of energy levels and approximate wave functions.