Abstract
We consider one dimensional Schrödinger operators
\begin{equation*}
H_\lambda=-\frac{d^2}{dx^2}+U+ \lambda V_\lambda
\end{equation*}
with nonlinear dependence on the parameter $\lambda$ and study the small $\lambda$ behavior of eigenvalues. Potentials $U$ and $V_\lambda$ are real-valued bounded functions of compact support. Under some assumptions on $U$ and $V_\lambda$, we prove the existence of a negative eigenvalue that is absorbed at the bottom of the continuous spectrum as $\lambda\to 0$. We also construct two-term asymptotic formulas for the threshold eigenvalues.
Key words: 1D Schrödinger operator, coupling constant threshold, negative
eigenvalue, zero-energy resonance, half-bound state.
Full Text
Article Information
| Title | Eigenvalues of Schrödinger operators near thresholds: two term approximation |
| Source | Methods Funct. Anal. Topology, Vol. 26 (2020), no. 1, 76-87 |
| DOI | 10.31392/MFAT-npu26_1.2020.06 |
| MathSciNet |
MR4113583 |
| Milestones | Received 05/09/2019; Revised 31/10/2019 |
| Copyright | The Author(s) 2020 (CC BY-SA) |
Authors Information
Yuriy Golovaty
Department of Mechanics and Mathematics, Ivan Franko National University of Lviv, 1 Universytetska str., Lviv, 79000, Ukraine
Citation Example
Yuriy Golovaty, Eigenvalues of Schrödinger operators near thresholds: two term approximation, Methods Funct. Anal. Topology 26
(2020), no. 1, 76-87.
BibTex
@article {MFAT1290,
AUTHOR = {Yuriy Golovaty},
TITLE = {Eigenvalues of Schrödinger operators near thresholds: two term approximation},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {26},
YEAR = {2020},
NUMBER = {1},
PAGES = {76-87},
ISSN = {1029-3531},
MRNUMBER = {MR4113583},
DOI = {10.31392/MFAT-npu26_1.2020.06},
URL = {http://mfat.imath.kiev.ua/article/?id=1290},
}
