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Discrete spectrum of Schroedinger operators with oscillating decaying potentials

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Periodic and Ergodic Spectral Problems

We consider the Schroedinger operator $H_{ta W} = -Delta + ta W$, self-adjoint in $L2(Rd)$, $d geq 1$. Here $ta$ 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 $H_{ta W}$ near the origin, and due to the irregular decay of $ta W$, we encounter some non semiclassical phenomena; in particular, $H_{ta W}$ has less eigenvalues than suggested by the semiclassical intuition.

This talk is part of the Isaac Newton Institute Seminar Series series.

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