We consider convergence of an approximation method for the recovery of a rotationally symmetric potential PSI from the sequence of eigenvalues. In order to permit the consideration of 'rough' potentials PSI (having essentially H^-1 (0.1) regularity), we first indicate the appropriate interpretation of -DELTA + PSI (with boundary conditions) as a selfadjoint, densely defined operator on ETA := L^2(OMEGA) and then show a suitable continuous dependence on PSI for the relevant eigenvalues. The approach to the inverse problem is by the method of 'generalized interpolation' end, aasuming uniqueness, it is shown that one has convergence to the correct potential PSI (strongly, for an appropriate norm) for a sequence of computationally implementable approximations (P_C, ,N)