Spectral properties of higher order Anharmonic Oscillators
Författare
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.
Publiceringsår
2010
Språk
Engelska
Sidor
110-126
Publikation/Tidskrift/Serie
Journal of Mathematical Sciences
Volym
165
Issue
1
Dokumenttyp
Artikel i tidskrift
Förlag
Springer
Ämne
- Mathematics
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 1072-3374