Absorbing Boundary Conditions for Solving Stationary Schrödinger Equations

  • Pauline Klein
  • Xavier Antoine
  • Christophe Besse
  • Matthias Ehrhardt
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)


Using pseudodifferential calculus and factorization theorems we construct a hierarchy of novel absorbing boundary conditions (ABCs) for the stationary Schrödinger equation with general (linear and nonlinear) exterior potential V (x). Doing so, we generalize the well-known quantum transmitting boundary condition of Lent and Kirkner to the case of space-dependent potential. Here, we present a brief introduction into our new approach based on finite elements suitable for computing scattering solutions and bound states.


Absorb Boundary Condition Quantum Waveguide Transparent Boundary Condition Pseudodifferential Calculus Linear Scattering 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pauline Klein
    • 1
  • Xavier Antoine
    • 1
  • Christophe Besse
    • 2
  • Matthias Ehrhardt
    • 3
  1. 1.Institut Elie Cartan NancyNancy-Université, CNRS UMR 7502, INRIA CORIDA TeamVandoeuvre-lès-NancyFrance
  2. 2.Equipe Projet Simpaf – Inria CR Lille Nord Europe, Laboratoire Paul Painlevé, Unité Mixte de Recherche CNRS (UMR 8524), UFR de Mathématiques Pures et AppliquéesUniversité des Sciences et Technologies de LilleVilleneuve d’Ascq CedexFrance
  3. 3.Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fachbereich C Mathematik und NaturwissenchaftenBergische Universität WuppertalWuppertalGermany

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