Abstract
AbstractWe consider Schrödinger operators of the form $$H_R = - \,\text {{d}}^2/\,\text {{d}}x^2 + q + i \gamma \chi _{[0,R]}$$
H
R
=
-
d
2
/
d
x
2
+
q
+
i
γ
χ
[
0
,
R
]
for large $$R>0$$
R
>
0
, where $$q \in L^1(0,\infty )$$
q
∈
L
1
(
0
,
∞
)
and $$\gamma > 0$$
γ
>
0
. Bounds for the maximum magnitude of an eigenvalue and for the number of eigenvalues are proved. These bounds complement existing general bounds applied to this system, for sufficiently large R.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference35 articles.
1. Abramov, A.A., Aslanyan, A., Davies, E.B.: Bounds on complex eigenvalues and resonances. J. Phys. A Math. Gen. 34(1), 57–72 (2001)
2. Aljawi, S., Marletta, M.: On the eigenvalues of spectral gaps of matrix-valued Schrödinger operators. Numer. Algorithms 86, 637–657 (2020)
3. Bögli, S.: Schrödinger operator with non-zero accumulation points of complex eigenvalues. Commun. Math. Phys. 352(2), 629–639 (2017)
4. Bögli, S., Štampach, F.: On Lieb–Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators. J. Spectral Theory 11(3), 1391–1413 (2021)
5. Borichev, A., Frank, R., Volberg, A.: Counting eigenvalues of Schrödinger operator with complex fast decreasing potential. arXiv:1811.05591 (2019)
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1. Schrödinger Operators with Complex Sparse Potentials;Communications in Mathematical Physics;2022-04-05