Introduction to Semiclassical Methods for the Schrödinger Operator with a Large Electric Potential

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


In this chapter, we present one of the basic techniques for analyzing the ground state energy (also called lowest eigenvalue or principal eigenvalue) of a Schrödinger operator in the case when the electric potential V has nondegenerate minima, in the limit of large coupling constant B. This problem turns out to be a semiclassical problem.


Ground State Energy Quadratic Approximation Harmonic Approximation Decay Property Magnetic Potential 
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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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