On the spectrum of the two-particle Schrödinger operator with point potential: one dimensional case

Abstract

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