P. G. Grinevich, R. G. Novikov, “Multipoint scatterers with bound states at zero energy”, TMF, 2017, Volume 193, Number 2,Pages <nobr>309–314</nobr>

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TMF, 2017 Volume 193, Number 2, Pages 309–314 (Mi tmf9349)

This article is cited in 8 papers

Multipoint scatterers with bound states at zero energy

P. G. Grinevich^abc, R. G. Novikov^def

^a Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia
^b Lomonosov Moscow State University, Moscow, Russia
^c Moscow Institute for Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia
^d Centre de Mathématiques Appliquées, École Polytechnique, Palaiseau, France
^e Université-Paris Saclay, Paris, France
^f Institute of Earthquake Prediction Theory and Mathematical Geophysics, RAS, Moscow, Russia

Abstract: We study multipoint scatterers with bound states at zero energy in three-dimensional space. We construct examples of such scatterers with multiple zero eigenvalues or with strong multipole localization of zero-energy bound states.

Keywords: Schrödinger equation, multipoint scatterer, bound state, zero energy, localization.

Received: 12.10.2016

DOI: 10.4213/tmf9349

English version: Theoretical and Mathematical Physics, 2017, 193:2, 1675–1679

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