We study three-body Schrödinger operators in one and two dimensions modelling an exciton interacting with a charged impurity. We consider certain classes of multiplicative interaction potentials proposed in the physics literature. We show that if the impurity charge is larger than some critical value, then three-body bound states cannot exist. Our spectral results are confirmed by variational numerical computations based on projecting on a finite dimensional subspace generated by a Gaussian basis.

中文翻译：

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一维和二维杂质结合激子

我们在一维和二维中研究三体Schrödinger算子，以建模与带电杂质相互作用的激子。我们考虑物理学文献中提出的某些类别的乘法相互作用势。我们表明，如果杂质电荷大于某个临界值，那么三体结合态将不存在。我们的光谱结果通过基于在高斯基础上生成的有限维子空间上的投影的变分数值计算得到了证实。