In this paper we investigate the operator We obtain the asymptotic form of each eigenvalue of H β as β tends to infinity. We also get the asymptotic form of the number of negative eigenvalues of H β in the strong coupling asymptotic regime.
On an isoperimetric inequality for a Schrödinger operator depending on the curvature of a loop
✍ Scribed by Almut Burchard; Lawrence E. Thomas
- Publisher
- Springer-Verlag
- Year
- 2005
- Tongue
- English
- Weight
- 984 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1050-6926
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The spectrum and essential spectrum of the Schrödinger operator \(A+V\) on a complete manifold are studied. As applications, we determine the index of the catenoid of any dimension and the essential spectrum for several minimal submanifolds in the Euclidean space of the Jacobi operator arising from
## Abstract A general scheme for factorizing second‐order time‐dependent operators of mathematical physics is given, which allows a reduction of corresponding second‐order equations to biquaternionic equations of first order. Examples of application of the proposed scheme are presented for both con