Abstract

We investigate a family of Schrödinger operators \(H(K)\), \(K\in(-\pi,\pi]^{d}\) associated with a system of three quantum particles on the \(d\)-dimensional lattice \({\mathbb{Z}}^{d}\) interacting via short-range pair potentials. It’s shown that the essential spectrum of the three-particle discrete Schrödinger operator \(H(K)\), \(K\in(-\pi,\pi]^{d}\) consists of a finitely many bounded closed intervals.

中文翻译：

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具有近程势的三粒子离散薛定谔算符的本质谱

摘要

我们研究了一系列薛定谔算子\(H(K)\) , \(K\in(-\pi,\pi]^{d}\)与\(d\)上的三个量子粒子系统相关联维晶格\({\mathbb{Z}}^{d}\)通过短程对势相互作用。这表明三粒子离散薛定谔算子的本质谱\(H(K)\) , \ (K\in(-\pi,\pi]^{d}\)由有限多个有界闭区间组成。