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Spectral Analysis of Schrödinger Operators

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

Abstract

Let Ω be an open set in \(\mathbb{R}^n, {\rm A} = (A_1, A_2, \ldots, A_n)\) be a C vector field on \(\bar{\Omega}\), corresponding to the so-called magnetic potential, V (which may depend on B) be a C (\(\bar{\Omega}\)) real-valued function, corresponding to the electric potential, and B > 0 be a (large) parameter, playing the role of the strength of the magnetic field. The vector field A corresponds more intrinsically to a 1-form
$$\omega_{\rm A} = \sum\limits^n_{j=1} A_j dx_j.$$
(1.1)

Keywords

Quadratic Form Ground State Energy Essential Spectrum Form Domain Compact Resolvent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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