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ON THE SPECTRAL PROPERTIES OF THE SCHR[수식]ODINGER OPERATOR WITH A MATRIX POTENTIAL

Coskan|Karakilic
장전수학회 (Jangjeon Mathematical Society)|2009.10|Advanced Studies in Contemporary Mathematics|제19권 제2호|pp. 249-259

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참고문헌

키워드

perturbationNeumann conditionSchrodinger operator
주제분류수학

초록

We consider a matrix Schrodinger operator de ned in [수식] (Q) by the differential expression Lu = -△u + V u and the Neumann boundary condition, where Q is a d-dimensional paralellepiped, V is a matrix potential, d ≥ 2, m ≥ 2 . We study the spectral properties of L in the high energy region, that is, we obtain the high energy asymptotics of the eigenvalues of L.

Abstract

We consider a matrix Schrodinger operator de ned in [수식] (Q) by the differential expression Lu = -△u + V u and the Neumann boundary condition, where Q is a d-dimensional paralellepiped, V is a matrix potential, d ≥ 2, m ≥ 2 . We study the spectral properties of L in the high energy region, that is, we obtain the high energy asymptotics of the eigenvalues of L.

참고문헌 (15)

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  9. Karpeshina, Y, "Perturbation Theory for the Schrodinger Operator with a nonsmooth Periodic Potential", Math. USSR-Sb, 71, pp.701~123 (1992)
  10. Karpeshina, Y, "Perturbation series for the Schrodinger Operator with a Periodic Potential near Planes of Diffraction", Communication in Analysis and Geometry, 4(3), pp.339~413 (1996)
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  14. Veliev, O. A, "Asimptotic Formulas for the Eigenvalues of the Periodic Schrodinger Operator and the Bethe-Sommerfeld Conjecture", Functsional Anal. i Prilozhen, 21(2), pp.1~15 (1987)
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