We turn back to the well known problem of interpretation of the Schrodinger
operator with the pseudopotential being the first derivative of the Dirac
function. We show that the problem in its conventional formulation contains
hidden parameters and the choice of the proper selfadjoint operator is
ambiguously determined. We study the asymptotic behavior of spectra and
eigenvectors of the Hamiltonians with increasing smooth potentials perturbed by
short-range potentials. Appropriate solvable models are constructed and the
corresponding approximation theorems are proved.