File(s) not publicly available
Spectral properties in the low-energy limit of one-dimensional Schrödinger operators H = –d2/dx2 + V. The Case <1, V1> =? 0
In this paper we consider the Schrödinger operator H = –d2/dx2+ V in L2(R), where V satisfies an abstract short-range condition and the (solvability) condition <1, V1> =? 0. Spectral properties of H in the low-energy limit are analyzed. Asymptotic expansions for R(?) = (H – ?)–1 and the S-matrix S(?) are deduced for ? ? 0 and ? ? 0, respectively. Depending on the zero-energy properties of H, the expansions of R(?) take different forms. Generically, the expansions of R(?) do not contain negative powers; the appearance of negative powers in ?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 L2-functions.
History
Publication status
- Published
Journal
Mathematische NachrichtenISSN
0025-584XPublisher
John Wiley & SonsIssue
1Volume
238Page range
113-143Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2013-09-19Usage metrics
Categories
No categories selectedLicence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC