Perturbation Theory for the Periodic Multidimensional Schrodinger Operator and the Bethe-Sommerfeld Conjecture

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dc.creatorVeliev, O. A.
dc.date2006-10-23
dc.date.accessioned2026-07-07T07:28:29Z
dc.date.available2026-07-07T07:28:29Z
dc.descriptionIn this paper we obtain asymptotic formulas of arbitrary order for the Bloch eigenvalue and the Bloch function of the periodic Schrodinger operator of arbitrary dimension, when corresponding quasimomentum lies near a diffraction hyperplane. Besides, writing the asymptotic formulas for the Bloch eigenvalue and the Bloch function, when corresponding quasimomentum lies far from the diffraction hyperplanes, obtained in my previous papers in improved and enlarged form, we obtain the complete perturbation theory for the multidimensional Schrodinger operator with a periodic potential. Moreover, we estimate the measure of the isoenergetic surfaces in the high energy region which implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimension and arbitrary lattice.
dc.descriptionPublished in International Journal of Contemporary Mathematical Sciences, Vol.2, 2007, no.2, p.19-87
dc.identifierhttps://arxiv.org/abs/math-ph/0610057
dc.identifierhttp://arxiv.org/abs/math-ph/0610057
dc.identifierInt. Journal of Contemporary Mathematical Sciences, Vol.2, 2007, no.2, p.19-87
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117749
dc.subjectMathematical Physics
dc.subject47F05, 35P15
dc.titlePerturbation Theory for the Periodic Multidimensional Schrodinger Operator and the Bethe-Sommerfeld Conjecture
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