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On the energy of bound states for magnetic Schrödinger operators

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  • Department of Mathematical Sciences
We provide a leading order semiclassical asymptotics of the energy of bound states for magnetic Neumann Schrödinger operators in two-dimensional (exterior) domains with smooth boundaries. The asymptotics is valid all the way up to the bottom of the essential spectrum. When the spectral parameter is varied near the value where bound states become allowed in the interior of the domain, we show that the energy has a boundary and a bulk component. The estimates rely on coherent states, in particular on the construction of ‘boundary coherent states’, and magnetic Lieb–Thirring estimates.
Original languageEnglish
JournalJournal of the London Mathematical Society
Pages (from-to)233-255
Number of pages23
Publication statusPublished - 2009

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