Models in Dimension 3: \(\mathbb{R}^3\) or \(\mathbb{R}^{3,+}\)

  • Søren Fournais
  • Bernard Helffer
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 77)


In the analysis of the magnetic Schrödinger operator with Neumann boundary condition in an open set\(\Omega \subset \mathbb{R}^3\), the first two models to analyze are the constant field case in \(\mathbb{R}^{3}\) and the constant field case in \(\mathbb{R}^{3,+}\). The latter model will permit us to understand the effect of the boundary.


Neumann Boundary Condition Strict Inequality Essential Spectrum Lower Eigenvalue Gauge Choice 
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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesAarhus UniversityAarhus CDenmark
  2. 2.Département de MathématiquesUniversité Paris-Sud and CNRSOrsay CedexFrance

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