  I study some possibilities of analytically solving a particular
Sturm-Liouville problem with step-wise (piece-constant) coefficients with help
of an iterative procedure mentioned in my previous paper (Green's function sum
rules). I construct short, simple, but very accurate analytical formulae for
calculating the ground state eigenvalue and eigenfunction as well as for
calculating the first eigenfunction. I study numerical precision of the
obtained approximations together with the perturbation theory results.
