Eigenvalue behaviors of Schrödinger operator defined on n-dimensional lattice with n + 1 delta potentials is studied. It can be shown that lower threshold eigenvalue and lower threshold resonance are appeared for n ≥ 2, and lower super-threshold resonance appeared for n = 1.where δ xs is the Kronecker delta.

In the paper a one-dimensional two-particle quantum system interacted by two identical point interactions is considered. The corresponding Schr\"{o}\-dinger operator (energy operator) $h_\varepsilon$ depending on $\varepsilon,$ is constructed as a self-adjoint extension of the symmetric Laplace operator. The main results of the work are based to the study of the operator $h_\varepsilon.$ First the essential spectrum is described. The existence of unique negative eigenvalue of the Schr\"{o}dinger operator is proved. Further, this eigenvalue and corresponding eigenfunction are found.

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