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Discrete spectrum of Schroedinger operators with oscillating decaying potentials

Tuesday 3rd February 2015 - 14:00 to 15:00
INI Seminar Room 2
We consider the Schroedinger operator $H_{\eta W} = -\Delta + \eta W$, self-adjoint in $L^2(R^d)$, $d \geq 1$. 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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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons