On the Spectrum of the Two-particle Shrödinger Operator with Point Interaction
Zahriddin MuminovUzbek–Israel Joint Faculty, National University of Uzbekistan, 100174, Tashkent, UzbekistanУткир КулжановFaculty of Mathematics, Samarkand State University, 703004, Samarkand, UzbekistanSh. S. LakaevUzbek–Israel Joint Faculty, National University of Uzbekistan, 100174, Tashkent, Uzbekistan
ABI
Аннотация
We consider a one-dimensional two-particle quantum system interacted by two identical point interactions situated symmetrically with respect to the origin at the points $$\pm x_{0}$$ . The corresponding Schrödinger operator (energy operator) is constructed as a self-adjoint extension of the symmetric Laplace operator. An essential spectrum is described and the condition for the existence of the eigenvalue of the Schrödinger operator is studied. The main results of the work are based on the study of the operator extension spectrum of the operator $$h_{\mu}.$$
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