Spectral properties in the low-energy limit of one-dimensional Schrodinger operators H = -d(2)/dx(2)+V. The case < 1,V1 > not equal 0
2002 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 238, 113-143 p.Article in journal (Refereed) Published
In this paper we consider the Schrodinger operator H = -d(2)/dx(2)+V in L-2(R), where V satisfies an abstract short-range condition and the (solvability) condition <1, V1>not equal0. Spectral properties of H in the low-energy limit are analyzed. Asymptotic expansions for R(zeta) = (H-zeta)(-1) and the S-matrix S(lambda) are deduced for zeta-->0 and lambdadown arrow0, respectively. Depending on the zero-energy properties of H, the expansions of R(C) take different forms. Generically, the expansions of R() do not contain negative powers; the appearance of negative powers in zeta(1/2) is due to the possible presence of zero-energy resonances (half-bound states) or the eigenvalue zero of H (bound state), or both. It is found that there are at most two zero resonances modulo L-2-functions.
Place, publisher, year, edition, pages
2002. Vol. 238, 113-143 p.
IdentifiersURN: urn:nbn:se:uu:diva-174119DOI: 10.1002/1522-2616(200205)238:1<113::AID-MANA113>3.3.CO;2-4ISI: 000175944900008OAI: oai:DiVA.org:uu-174119DiVA: diva2:526501