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Author Gridnev, Dmitry K.
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2009-12-02
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics
Subject Keyword Mathematical Physics ♦ 35J10 ♦ math ♦ physics:math-ph
Abstract We consider a 3--body system in $\mathbb{R}^3$ with non--positive potentials and non--negative essential spectrum. Under certain requirements on the fall off of pair potentials it is proved that if at least one pair of particles has a zero energy resonance then a square integrable zero energy ground state of three particles does not exist. This complements the analysis in \cite{1}, where it was demonstrated that square integrable zero energy ground states are possible given that in all two--body subsystems there is no negative energy bound states and no zero energy resonances. As a corollary it is proved that one can tune the coupling constants of pair potentials so that for any given $R, \epsilon >0$: (a) the bottom of the essential spectrum is at zero; (b) there is a negative energy ground state $\psi(\xi)$, where $\int \psi(\xi) ^2 = 1$; (c) $\int_{ \xi \leq R} \psi(\xi) ^2 < \epsilon$.
Educational Use Research
Learning Resource Type Article


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