Abstract

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 \(h_{\mu}.\)

中文翻译：

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点相互作用的两粒子Shrödinger算子的谱

摘要

我们考虑一维两粒子量子系统，该系统由两个相同的点相互作用（相对于原点\（\ pm x_ {0} \）对称地相互作用）相互作用。相应的Schrödinger算子（能量算子）被构造为对称Laplace算子的自伴随扩展。描述了一个基本谱，并研究了Schrödinger算子特征值存在的条件。这项工作的主要结果是基于对算子\（h _ {\ mu}。\）的算子扩展谱的研究。