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Discrete spectrum of Schrodinger operators with oscillating decaying potentials

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 نشر من قبل Georgi Raikov
 تاريخ النشر 2015
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Georgi Raikov




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We consider the Schrodinger operator $H_{eta W} = -Delta + eta W$, self-adjoint in $L^2({mathbb R}^d)$, $d geq 1$. Here $eta$ is a non constant almost periodic function, while $W$ decays slowly and regularly at infinity. We study the asymptotic behaviour of the discrete spectrum of $H_{eta W}$ near the origin, and due to the irregular decay of $eta W$, we encounter some non semiclassical phenomena. In particular, $H_{eta W}$ has less eigenvalues than suggested by the semiclassical intuition.



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