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 (Greens 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.
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