For an extremely elementary example of an ordinary differential
radial Schroedinger equation with potential $V(r)=ar^ + br^4 +
cr^6$ (tractable, of course, by virtually any commercially
available software), a few samples of the ground-state wave
function $\psi(r)$ are constructed, for some hardly comprehensible
reasons, using an unbelievably complicated iterative recipe
proposed, by the same author, in refs. [1] and [6].
MR2454519 Zhao, Wei-Qin Two kinds of iterative solutions for
generalized sombrero-shaped potential in $N$-dimensional space. J.
Phys. A 41 (2008), no. 23, 235302, 12 pp. 81Q05 (65Nxx 81-04)