Discrete spectrum of Schr "odinger operators with oscillating decaying\n potentials

2015/01/27 by Georgi Raikov, Raikov, Georgi
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1501.06865

Abstract

We consider the Schr "odinger operator H_{\η W} = -\Δ + \η W,\nself-adjoint in L²( mathbb R^d), d \≥ 1. Here \η is a non constant\nalmost periodic function, while W decays slowly and regularly at infinity. We\nstudy the asymptotic behaviour of the discrete spectrum of H_{\η W} near\nthe origin, and due to the irregular decay of \η W, we encounter some non\nsemiclassical phenomena. In particular, H_{\η W} has less eigenvalues than\nsuggested by the semiclassical intuition.\n

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