Geometriae Dedicata

, Volume 91, Issue 1, pp 155–173

Semiclassical Asymptotics and Gaps in the Spectra of Magnetic Schrödinger Operators

  • V. Mathai
  • M. Shubin

DOI: 10.1023/A:1016245930716

Cite this article as:
Mathai, V. & Shubin, M. Geometriae Dedicata (2002) 91: 155. doi:10.1023/A:1016245930716


In this paper, we study an L2 version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant μ goes to zero.

magnetic Schrödinger operators spectral gaps semiclassical approximation Morse potentials 

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • V. Mathai
    • 1
    • 2
  • M. Shubin
    • 3
  1. 1.Department of MathematicsUniversity of AdelaideAdelaideAustralia
  2. 2.Department of MathematicsMITCambridgeU.S.A.
  3. 3.Department of MathematicsNortheastern UniversityBostonU.S.A.

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