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Perturbation theory for the decay rate of eigenfunctions in the generalized \(N\)-body problem. (English) Zbl 0819.35105

Summary: Simple examples are known where eigenfunctions decay faster than the usual upper bounds would lead one to believe. We develop aspects of the perturbation theory of the decay rate of eigenfunctions as measured by radial exponential weights. We show that generically (in a Baire category sense) eigenfunction decay rates are governed by the lowest threshold.

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
47A55 Perturbation theory of linear operators
81U10 \(n\)-body potential quantum scattering theory
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