The trick with the lowering of the order of differential equation is
applied replacing the standard Schroedinger quantum Woods-Saxon
bound-state eigenvalue problem by its Riccati-equation
representation. The related oscillation theorems and an efficient
approximation of the centrifugal term are then used for an efficient
approximate evaluation and study of degeneracies between levels with
various orbital quantum numbers and spatial dimensions.


MR2673637 Ikhdair, Sameer M.; Sever, Ramazan Any $l$-state solutions
of the Woods-Saxon potential in arbitrary dimensions within the new
improved quantization rule. Internat. J. Modern Phys. A 25 (2010),
no. 20, 3941--3952. 81Qxx