Spectral properties of higher order Anharmonic Oscillators
(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:
https://lup.lub.lu.se/record/4221736
- author
- Helffer, Bernard and Persson Sundqvist, Mikael LU
- publishing date
- 2010
- 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}}, }