Smooth transformations of Kratzer’s potential in N dimensions

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Abstract
We study smooth transformations V(r)=g(−1/r)+f(1/r 2 ) of Kratzer’s potential −a/r+b/r 2 in N⩾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⩾2, corresponding, respectively, to the two cases that the transformation functions g and f are either both convex (g ″ ⩾0) and f ″ ⩾0) or both concave (g ″ ⩽0 and f ″ ⩽0). Detailed results are presented for V(r)=−a/r+b/r β and V(r)=−(v/r)[1−ar/(1+r)]+b/r 2 .