WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials
Publication
, Journal Article
Christ, M; Kiselev, A
Published in: Journal of Functional Analysis
February 1, 2001
We prove the WKB asymptotic behavior of solutions of the differential equation -d2u/dx2+V(x)u=Eu for a.e. E>A where V=V1+V2, V1∈Lp(R), and V2 is bounded from above with A=limsupx→∞V(x), while V′2(x)∈Lp(R), 1≤p<2. These results imply that Schrödinger operators with such potentials have absolutely continuous spectrum on (A, ∞). We also establish WKB asymptotic behavior of solutions for some energy-dependent potentials. © 2001 Academic Press.
Duke Scholars
Published In
Journal of Functional Analysis
DOI
ISSN
0022-1236
Publication Date
February 1, 2001
Volume
179
Issue
2
Start / End Page
426 / 447
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Christ, M., & Kiselev, A. (2001). WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials. Journal of Functional Analysis, 179(2), 426–447. https://doi.org/10.1006/jfan.2000.3688
Christ, M., and A. Kiselev. “WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials.” Journal of Functional Analysis 179, no. 2 (February 1, 2001): 426–47. https://doi.org/10.1006/jfan.2000.3688.
Christ M, Kiselev A. WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials. Journal of Functional Analysis. 2001 Feb 1;179(2):426–47.
Christ, M., and A. Kiselev. “WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials.” Journal of Functional Analysis, vol. 179, no. 2, Feb. 2001, pp. 426–47. Scopus, doi:10.1006/jfan.2000.3688.
Christ M, Kiselev A. WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials. Journal of Functional Analysis. 2001 Feb 1;179(2):426–447.
Published In
Journal of Functional Analysis
DOI
ISSN
0022-1236
Publication Date
February 1, 2001
Volume
179
Issue
2
Start / End Page
426 / 447
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics