Harmonic oscillator perturbed by a decreasing scalar potential
In this paper we study the perturbation L = H + V , where H = - d 2 m d x 2 m + x 2 m on R , m ∈ N ∗ and V is a decreasing scalar potential. Let λ k be the k th eigenvalue of H . We suppose that the eigenvalues of L around λ k can be written in the form λ k + μ k . The main result of the paper is an...
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Published in | Journal of pseudo-differential operators and applications Vol. 11; no. 1; pp. 141 - 157 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
01.03.2020
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | In this paper we study the perturbation
L
=
H
+
V
, where
H
=
-
d
2
m
d
x
2
m
+
x
2
m
on
R
,
m
∈
N
∗
and
V
is a decreasing scalar potential. Let
λ
k
be the
k
th
eigenvalue of
H
. We suppose that the eigenvalues of
L
around
λ
k
can be written in the form
λ
k
+
μ
k
. The main result of the paper is an asymptotic formula for fluctuation
{
μ
k
}
which is given by a transformation of
V
. In the case
m
=
1
we recover a result on the harmonic oscillator. |
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ISSN: | 1662-9981 1662-999X |
DOI: | 10.1007/s11868-019-00284-4 |