Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

We provide benchmark values for Shannon information entropies in position space for the ground state and ls2s S-1(e) excited state of helium confined with finite confinement potentials by employing the highly correlated Hylleraas-type wave functions. For the excited state, a tilt (small oscillation) on the curve of Shannon entropy as a function of width size for the confinement potential is observed. Justified by the behavior of the electron density, the localization or delocalization of the helium wave functions confined with repulsive and attractive finite oscillator (FO) potentials are examined.