On the Spectrum of the Two-Particle Schrödinger Operator with Point Potential: Two Dimensional Case

In the article, a two-dimensional two-particle quantum system interacted by two identical point interactions is studied. The corresponding Schrödinger operator (energy operator) $$h_{\mu}$$ depending on $$\mu$$ is constructed as a self-adjoint extension of the symmetric Laplace operator. The essential spectrum of $$h_{\mu}$$ is described. The existence of unique eigenvalue of the Schrödinger operator is proved and corresponding eigenfunction to this eigenvalue is found.