Suppose for some specific problem (symmetric potential well) the Schroedinger equation is expected to give certain discrete bound states and corresponding eigenfunctions. Now I am trying to obtain the eigenfunctions by numerically solving the equation and plotting the solutions by randomly assigning energy value. In general most of the times my guess of energy value will be wrong but the program (say Mathematica) will give some result (plot for the wave function). What will be interpretation for those results? The answer may be those are simply wrong eigenfunctions so no interpretation is needed. However I was doing this stupid job and was getting divergent wave functions almost always. But I do not understand why Mathematica was giving divergent plot rather than some arbitrary finite plot. Do you have any clue?