This article is cited in 3 papers

MATHEMATICS

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

Utkir N. Kuljanov

Samarkand State University, Samarkand, Uzbekistan

Abstract: In the paper, a one-dimensional two-particle quantum system interacted by two identical point interactions is considered. The corresponding Schrödinger 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 on the study of the operator $h_\varepsilon$. First, the essential spectrum is described. The existence of unique negative eigenvalue of the Schrödinger operator is proved. Further, this eigenvalue and the corresponding eigenfunction are found.

Keywords: two-particle quantum system, symmetric Laplace operator, eigenvalue, eigenfunction, energy operator.

Received: 19.08.2022
Revised: 18.09.2023
Accepted: 19.09.2023

Language: English

DOI: 10.17586/2220-8054-2023-14-5-505-510

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