Wave Functions for1s2s S1Helium

The $1s2s{}_{}{}^1{}_{}{}^{}S$ state of He has been treated with a variant of Hylleraas' variational method, and a wave function has been determined which gives an error of only 0.005 ev in the energy of the system. The properties of desirable functions for use in this method are discussed. Wave functions of the Hartree and Fock types, and a more flexible function not involving $r_{12}$, are also determined by simple variational processes. The properties of the resulting functions are compared, and are discussed in the light of the polarization method of Hylleraas and Bethe, properly applicable to more highly excited states. The computations by the polarization method have been extended, and the results are compared with those given by the variational procedure.