On the spectrum of partially periodic operators
2007 (English)In: Operator Theory, Analysis and Mathematical Physics / [ed] Janas, J; Kurasov, P; Laptev, A; Naboko, S; Stolz, G, BASEL: BIRKHAUSER VERLAG AG , 2007, Vol. 174, 35-50 p.Conference paper (Refereed)
We consider Schrodinger operators H = -Delta + V in L-2 (Omega) where the domain Omega subset of R-+(d+1) and the potential V = V (x, y) are periodic with respect to the variable x is an element of R-d. We assume that Omega is unbounded with respect to the variable y is an element of R and that V decays with respect to this variable. V may contain a singular term supported on the boundary. We develop a scattering theory for H and present an approach to prove absence of singular continuous spectrum. Moreover, we show that certain repulsivity conditions on the potential and the boundary of Omega exclude the existence of surface states. In this case, the spectrum of His purely absolutely continuous and the scattering is complete.
Place, publisher, year, edition, pages
BASEL: BIRKHAUSER VERLAG AG , 2007. Vol. 174, 35-50 p.
, OPERATOR THEORY : ADVANCES AND APPLICATIONS, ISSN 0378-620X ; 174
scattering theory, periodic operator, Schrodinger operator
Physical Sciences Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-39387DOI: 10.1007/978-3-7643-8135-6_4ISI: 000246202600004ISBN: 978-3-7643-8134-9OAI: oai:DiVA.org:kth-39387DiVA: diva2:440762
International Conference on Operator Theory and Its Applications in Mathematical Physics. Bedlewo, POLAND. JUL , 2004