Spectral Properties of the Periodic Magnetic Schr�dinger Operator in the High-Energy Region. Two-Dimensional Case

Autor:	Yulia Karpeshina
Rok vydání:	2004
Předmět:	Conjecture Partial differential equation Operator (physics) Statistical and Nonlinear Physics Mathematics::Spectral Theory Eigenfunction Space (mathematics) symbols.namesake Quantum mechanics symbols Mathematical Physics Eigenvalues and eigenvectors Schrödinger's cat Bloch wave Mathematics
Zdroj:	Communications in Mathematical Physics. 251:473-514
ISSN:	1432-0916 0010-3616
DOI:	10.1007/s00220-004-1129-0
Popis:	The goal is to investigate spectral properties of the operator H=(−i∇ +a(x))2+a0(x) in the two-dimensional situation, a(x), a0(x)) being periodic. We construct asymptotic formulae for Bloch eigenvalues and eigenfunctions in the high-energy region, describe properties of isoenergetic curves in the space of quasimomenta and give a new proof of the Bethe-Sommerfeld conjecture.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c245047e69ed3e5038603d8e52942301 https://doi.org/10.1007/s00220-004-1129-0 Zobrazit plný text záznamu Plný text ve formátu PDF