On the convergence of eigenfunctions to threshold energy states

preprint2006arXivOpen access

Abstract

We prove the convergence in certain weighted spaces in momentum space of eigenfunctions of H = T-lambda*V as the energy goes to an energy threshold. We do this for three choices of kinetic energy T, namely the non-relativistic Schr"odinger operator, the pseudorelativistc operator sqrt{-Δ+m^2}-m, and the Dirac operator.

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