A Lower Limit for the Theoretical Energy of the Normal State of Helium

Abstract

The method of using a modification of Weinstein's lower limit for the energy, as given recently by one of the authors, has been applied to the normal state of helium, with the same sequence of functions as was employed by Hylleraas in his upper limit calculations. The ninth approximation leads to the lower limit -1.45508 Hylleraas units, which can very probably be increased to -1.45446, whereas the upper limit found by Hylleraas is -1.45187. The bearing of the results found on the probable location of the true eigenvalue is discussed, as is also the applicability of the method in general.