Electron density and its derivatives at the nucleus for spherically confined hydrogen atom

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 $\left[{\eta_l^{\prime\prime} (0)\over\eta_l(0)}\right]$ . Here, the conventional spherical density $\overline\varrho$ ( r ) is scaled as η l ( r ) = ${\bar{\varrho} (r)\over r^{2l}}$ 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 1 s , 2 s , 2 p , and 3 d 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. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009