Annales Henri Poincaré

, Volume 16, Issue 7, pp 1651–1688 | Cite as

Accurate Semiclassical Spectral Asymptotics for a Two-Dimensional Magnetic Schrödinger Operator

  • Bernard Helffer
  • Yuri A. KordyukovEmail author


We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schrödinger operator on a two-dimensional Riemannian manifold. We suppose that the minimal value b 0 of the intensity of the magnetic field is strictly positive, and the corresponding minimum is unique and non-degenerate. The purpose is to get the control on the spectrum in an interval \({(hb_0, h(b_0 + \gamma_0)]}\) for some \({\gamma_0 > 0}\) independent of the semiclassical parameter h. The previous papers by Helffer–Mohamed and by Helffer–Kordyukov were only treating the ground-state energy or a finite (independent of h) number of eigenvalues. Note also that N. Raymond and S. Vũ Ngọc have recently developed a different approach of the same problem.


Selfadjoint Operator Principal Symbol Semiclassical Analysis Weyl Quantization Weyl Symbol 
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Authors and Affiliations

  1. 1.Département de Mathématiques, Bâtiment 425Univ. Paris-Sud et CNRSOrsay CédexFrance
  2. 2.Institute of MathematicsRussian Academy of SciencesUfaRussia

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