The Point Spectrum of the Three-Particle Schrödinger Operator on $$\boldsymbol{\mathbb{Z}}$$ with Masses $$\boldsymbol{m_{1}=m_{2}=\infty}$$ and $$\boldsymbol{m_{3}<\infty}$$

Abstract

In this article, the hamiltonian $$H(K)$$ of a system of three-particles moving on the lattice $$\mathbb{Z}$$ interacting through repulsive or attractive zero-range pairwise potentials is considered. It is studied the point spectrum of the Schrödinger operator which possesses infinitely many eigenvalues depending on repulsive or attractive interactions, assuming that two particles in the system have infinite mass.

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DOI

10.1134/s1995080224606817

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