Accurate Calculations of Radial Expectations Values ⟨r-2⟩ for Confined Hydrogen-Like Atoms and Isotropic Harmonic Oscillator

By attaining an accuracy of 30 significant figures, in the present work we have calculated the expectation values of ⟨ r - 2 ⟩ of a few states for the confined hydrogen atom and the confined harmonic oscillator, as a function of the confinement radius R c . In comparison to other calculations reported in the literature, our results are found to be more accurate. This numerical precision was achieved by using the exact wave function of each system.