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On the convergence of eigenfunctions to threshold energy states

Published online by Cambridge University Press:  05 February 2008

Thomas Østergaard Sørensen  and
Edgardo Stockmeyer
Thomas Østergaard Sørensen
Affiliation:
Laboratoire de Mathématiques, Université Paris-Sud, Bât. 425, 91405 Orsay Cedex, France and Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, Denmark (sorensen@math.aau.dk)
Edgardo Stockmeyer
Affiliation:
Mathematisches Institut, Universität München, Theresienstrasse 39, 80333 Munich, Germany (stock@mathematik.uni-muenchen.de)
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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 Schrödinger operator, the pseudorelativistc operator $\sqrt{-\Delta+m^2}-m$, and the Dirac operator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 1 , February 2008 , pp. 169 - 187
Copyright
2008 Royal Society of Edinburgh

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