  We show that the conditional shape invariance symmetry can be used as a very
powerful tool to calculate the eigenvalues of the mixed potential V (r) = ar +
br^2 +c/r + l(l+1)/r^2 for a restricted set of potential parameters. The energy
for any state can be obtained algebraically, albeit for a severely restricted
set of potential parameters. We also indicate that each member of the hierarchy
of Hamiltonians is basically conditionally translational shape invariant.
Comparison of analytically obtained results with numerical results is also
presented. Our present methodology can be taken as an alternative treatment for
the calculation of any higher order excited states of conditionally exactly
solvable (CES) potentials.
