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The Efimov effect of three-body Schrödinger operators. (English) Zbl 0761.35078
The author considers three-body Schrödinger operators, with pair potentials decaying at infinity like \(| x|^{-\rho}\) with \(\rho>2\).
Assuming that all two-particles subsystems have no negative bound states but a zero resonance energy, it is proved that the whole system has an infinite number of negative bound states energies, accumulating at zero (Efimov effect).

MSC:
35P25 Scattering theory for PDEs
35P20 Asymptotic distributions of eigenvalues in context of PDEs
81U10 \(n\)-body potential quantum scattering theory
35Q40 PDEs in connection with quantum mechanics
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References:
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