Smooth transformations of Kratzer's potential in N dimensions

We study smooth transformations V(r) = g(- 1/r) + f(1/r(2)) of Kratzer's potential -a/r + b/r(2) in N greater than or equal to 2 spatial dimensions. Eigenvalue approximation formulas are obtained which provide lower or upper energy bounds for all the discrete energy eigenvalues E(nl) and all N greater than or equal to 2, corresponding, respectively, to the two cases that the transformation functions g and f are either both convex (g "greater than or equal to 0) and f "greater than or equal to 0) or both concave (g "less than or equal to 0 and f "less than or equal to 0). Detailed results are presented for V(r) = - a/r + b/r(beta) and V(r)= -(nu/r)[1 - ar/(1 + r)] + b/r(2). (C) 1998 American Institute of Physics. [S0021-9606(98)00332-8].