Accurate Calculations of Radial Expectations Values $$\varvec{\langle {r^{ - 2}}\rangle }$$ for Confined Hydrogen-Like Atoms and Isotropic Harmonic Oscillator

Abstract

By attaining an accuracy of 30 significant figures, in the present work we have calculated the expectation values of $$\langle {r^{ - 2}}\rangle $$ 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.