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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
and
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
2016-04-01 11:10:43
date last changed
2022-01-26 06:01:39
@article{3c6b6689-94f9-4668-967f-988c261b1f17,
  abstract     = {{We discuss spectral properties of the selfadjoint operator<br/>−<br/>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<br/>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.}},
  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}},
  doi          = {{10.1007/s10958-010-9784-5}},
  volume       = {{165}},
  year         = {{2010}},
}