Spectral Analysis of Schrödinger Operators

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


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
$$\omega_{\rm A} = \sum\limits^n_{j=1} A_j dx_j.$$


Quadratic Form Ground State Energy Essential Spectrum Form Domain Compact Resolvent 
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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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