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We show that the conditional shape invariance symmetry can be used as a verypowerful 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 energyfor any state can be obtained algebraically, albeit for a severely restrictedset of potential parameters. We also indicate that each member of the hierarchyof Hamiltonians is basically conditionally translational shape invariant.Comparison of analytically obtained results with numerical results is alsopresented. Our present methodology can be taken as an alternative treatment forthe calculation of any higher order excited states of conditionally exactlysolvable (CES) potentials.

Application of conditional shape invariance symmetry to obtain the eigen-spectrum of the mixed potential V (r) = ar + br^2 + c/r + l(l+1)/r^2