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We turn back to the well known problem of interpretation of the Schrodingeroperator with the pseudopotential being the first derivative of the Diracfunction. We show that the problem in its conventional formulation containshidden parameters and the choice of the proper selfadjoint operator isambiguously determined. We study the asymptotic behavior of spectra andeigenvectors of the Hamiltonians with increasing smooth potentials perturbed byshort-range potentials. Appropriate solvable models are constructed and thecorresponding approximation theorems are proved. We introduce the concepts ofthe resonance set and the coupling function, which are spectral characteristicsof the shape of squeezed potentials. The selfadjoint operators in the solvablemodels are determined by means of the resonance set and the coupling function.

Solvable models for the Schrodinger operators with $\delta'$-like potentials