  In a recent paper [1] we have proposed a new approach for extracting the wave
function of the $\pi$-meson $\varphi_{\pi}(x)$ and the masses and
  wave functions of its first resonances from the new QCD sum rules for
non-diagonal correlators obtained in [2]. Here, we test our approach using an
exactly solvable toy model as an illustrating example. We demonstrate the
validity of the method and suggest a pure algebraic procedure for extracting
the masses and wave functions relating to the case under investigation. We also
explore the stability of the procedure under perturbations of the theoretical
part of the sum rule. In application to the pion case, this results not only in
the mass and wave function of the first resonance ($\pi'$), but also in the
estimation of $\pi''$-mass.
