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Spectral properties of higher order Anharmonic Oscillators

Helffer, Bernard and Persson Sundqvist, Mikael LU (2010) In Journal of Mathematical Sciences 165(1). p.110-126
Abstract
We discuss spectral properties of the selfadjoint operator



d

2

dt

2

+

t

k

+1

k

+1



α

2

in

L

2

(

R

)

for odd integers

k

. We prove that the minimum over

α

of the ground state energy of

this operator is attained at a unique point which tends to zero as

k

tends to infinity. We

also show that the minimum is nondegenerate. These questions arise naturally in the

spectral analysis of Schr ̈

odinger operators with magnetic field.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Sciences
volume
165
issue
1
pages
110 - 126
publisher
Springer
external identifiers
  • scopus:77949299791
ISSN
1072-3374
DOI
10.1007/s10958-010-9784-5
language
English
LU publication?
no
id
3c6b6689-94f9-4668-967f-988c261b1f17 (old id 4221736)
date added to LUP
2014-02-03 14:16:57
date last changed
2018-07-01 03:23:56
@article{3c6b6689-94f9-4668-967f-988c261b1f17,
  abstract     = {We discuss spectral properties of the selfadjoint operator<br/><br>
−<br/><br>
d<br/><br>
2<br/><br>
dt<br/><br>
2<br/><br>
+<br/><br>
t<br/><br>
k<br/><br>
+1<br/><br>
k<br/><br>
+1<br/><br>
−<br/><br>
α<br/><br>
2<br/><br>
in<br/><br>
L<br/><br>
2<br/><br>
(<br/><br>
R<br/><br>
)<br/><br>
for odd integers<br/><br>
k<br/><br>
. We prove that the minimum over<br/><br>
α<br/><br>
of the ground state energy of<br/><br>
this operator is attained at a unique point which tends to zero as<br/><br>
k<br/><br>
tends to infinity. We<br/><br>
also show that the minimum is nondegenerate. These questions arise naturally in the<br/><br>
spectral analysis of Schr ̈<br/><br>
odinger operators with magnetic field.},
  author       = {Helffer, Bernard and Persson Sundqvist, Mikael},
  issn         = {1072-3374},
  language     = {eng},
  number       = {1},
  pages        = {110--126},
  publisher    = {Springer},
  series       = {Journal of Mathematical Sciences},
  title        = {Spectral properties of higher order Anharmonic Oscillators},
  url          = {http://dx.doi.org/10.1007/s10958-010-9784-5},
  volume       = {165},
  year         = {2010},
}