Spectrum of a model three-particle Schrödinger operator

Yu. Kh. Èshkabilov

Faculty of Mechanics and Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: We study the spectrum of a model three-particle Schrödinger operator $H(\varepsilon)$, $\varepsilon>0$. We prove that for a sufficiently small $\varepsilon>0$, this operator has no bound states and no two-particle branches of the spectrum. We also obtain an estimate for the small parameter $\varepsilon$.

Keywords: Schrödinger operator, spectrum, essential spectrum, discrete spectrum.

Received: 27.02.2015
Revised: 05.05.2015

DOI: 10.4213/tmf8879

 English version: Theoretical and Mathematical Physics, 2016, 186:2, 268–279

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