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The work is devoted to the study of Laplace operator when the potential is asingular generalized function and plays the role of a singular perturbation ofa Laplace operator. Abstract theorem obtained earlier by the authors B.N.Biyarov and G.K. Abdrasheva applies to this. The main purpose of the study isthe spectral issue. Singular perturbations for differential operators have beenstudied by many authors for the mathematical substantiation of solvable modelsof quantum mechanics, atomic physics, and solid state physics. In all thesecases, the problems were self-adjoint. In this paper, we considernon-self-adjoint singular perturbation problems. A new method has beendeveloped that allows investigating the considered problems.

Correct Singular Perturbations of the Laplace Operator with the Spectrum of the Unperturbed Operator