  The generalized pseudospectral method is employed to study spherical
confinement in two simple Coulombic systems: (i) well celebrated and heavily
studied H atom (ii) relatively less explored Hulth\'en potential. In both
instances, arbitrary cavity size, as well as low and higher states are
considered. Apart from bound state eigenvalues, eigenfunctions, expectation
values, quite accurate estimates of the critical cage radius for H atom for all
the 55 states corresponding to $n \leq 10$, are also examined. Some of the
latter are better than previously reported values. Degeneracy and energy
ordering under the isotropic confinement situation are discussed as well. The
method produces consistently high-quality results for both potentials for small
as well as large cavity size. For the H atom, present results are comparable to
best theoretical values, while for the latter, this work gives considerably
better estimates than all existing work so far.
