Local properties of three-body atomic wave functions

Abstract

The local properties and accuracy of the positronium negative-ion $({\mathrm{Ps}}^{\ensuremath{-}})$ ground-state wave functions obtained by the stochastic variational method (SVM) and by direct solution of the Schr\"odinger equation with the help of the correlation-function hyperspherical-harmonic method (CFHHM) are studied and compared. Though the energy, calculated by both methods, agrees to up to ten digits, the amplitudes of the values of the operator $D=H\ensuremath{\Psi}/E\ensuremath{\Psi}\ensuremath{-}1,$ characterizing local deviation of the wave function from its true value, in all of the coordinate space in the SVM are consistently larger (by up to five orders of magnitude) than in the CFHHM, despite the fact that the SVM observables except $〈\ensuremath{\delta}({\mathbf{r}}_{k})〉$ converge to significantly more digits than the CFHHM observables for their respective selected bases.