Exponential bounds and absence of positive eigenvalues forN-body Schrödinger operators

Abstract

For a large class ofN-body potentialsV we prove that if ϕ is an eigenfunction of −δ+V with eigenvalueE then sup{α²+E:α≧0, exp(α|x|)ϕ∈L ²} is either a threshold or +∞. Consequences of this result are the absence of positive eigenvalues and “optimal”L ²-exponential lower bounds.