Korean Journal of Mathematics

  • 제26권4호
  • /
  • Pages.601-614
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  • 2018
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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ABSOLUTE CONTINUITY OF THE MAGNETIC SCHRÖDINGER OPERATOR WITH PERIODIC POTENTIAL

  • Assel, Rachid (Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir)
  • 투고 : 2018.06.19
  • 심사 : 2018.11.22
  • 발행 : 2018.12.30
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초록

We consider the magnetic $Schr{\ddot{o}}dinger$ operator coupled with two different potentials. One of them is a harmonic oscillator and the other is a periodic potential. We give some periodic potential classes for which the operator has purely absolutely continuous spectrum. We also prove that for strong magnetic field or large coupling constant, there are open gaps in the spectrum and we give a lower bound on their number.

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참고문헌

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