ABSTRACT:It is shown that the energy of a hydrogen-like atom confined inside a spherical cavity of radius, R, and potential barrier, V 0 , is quantitatively defined by the ratio. Here, the conventional spherical density¯ (r) is scaled as η l (r) =¯ (r) r 2l and the ratio of the second derivative η l (r) to η l (r) is evaluated at the nucleus. Numerical results of the ratios are presented for 1s, 2s, 2p, and 3d states at several values of V 0 . For such states, the characteristic radii of confinement leading to the well-defined values of energy are identified.