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On the Stable Eigenvalues of Perturbed Anharmonic Oscillators in Dimension Two.
- Source :
- Communications in Mathematical Physics; Feb2022, Vol. 390 Issue 1, p309-348, 40p
- Publication Year :
- 2022
-
Abstract
- We study the asymptotic behavior of the spectrum of a quantum system which is a perturbation of a spherically symmetric anharmonic oscillator in dimension 2. We prove that a large part of its eigenvalues can be obtained by Bohr–Sommerfeld quantization rule applied to the normal form Hamiltonian and also admits an asymptotic expansion at infinity. The proof is based on the generalization to the present context of the normal form approach developed in Bambusi et al. (Commun Part Differ Equ 45:1–18, 2020) (see also Parnovski and Sobolev in Invent Math 181(3):467–540, 2010) for the particular case of T d . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 390
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 156445791
- Full Text :
- https://doi.org/10.1007/s00220-021-04301-w