Spectral properties of higher order Anharmonic Oscillators
Author
Summary, in English
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.
−
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.
Publishing year
2010
Language
English
Pages
110-126
Publication/Series
Journal of Mathematical Sciences
Volume
165
Issue
1
Document type
Journal article
Publisher
Springer
Topic
- Mathematics
Status
Published
ISBN/ISSN/Other
- ISSN: 1072-3374