Generic Simplicity of a Schrödinger-type Operator on the Torus
Louis Omenyi, Emmanuel Nwaeze, McSylvester Omaba
Asian Research Journal of Mathematics · pp. 1–19 · Published 11 Jan 2017
10.9734/ARJOM/2017/31160Abstract
The generic simplicity of the spectrum of a Schrödinger-type operator on the n-dimensional torus is studied using the Rayleigh-Schrödinger perturbation theory. The existence of a perturbation potential of the Laplacian is proved and suitable conditions on the potential that guarantee the generic simplicity of the spectrum constructed. It is also proved that with the potential, the degeneracy of the spectrum of the Laplacian on the n-dimensional torus splits at first order of the perturbation.
References (17)
- 1 Perturbation Theory for Linear Operators [DOI]
- 2 The Theory of Sound [DOI]
- 3 The Symmetric Eigenvalue Problem [DOI]
- 4 Eigenvalues in Riemannian Geometry [DOI]
- 5 Boundary Stabilization of Thin Plates [DOI]
- 6 The Schrödinger Equation [DOI]
- 7 Heat Kernel and Analysis on Manifolds [DOI]
- 8 Generic Properties of Eigenfunctions [DOI]
- 9 Introduction to spectral theory : with applications to Schrödinger operators
- 10 Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations [DOI]
- 11 Spectra of hyperbolic surfaces [DOI]
- 12 Genericity of simple eigenvalues for elliptic PDE’s [DOI]
- 13 Generic Simplicity of the Spectrum and Stabilization for a Plate Equation [DOI]
- 14 “Momentum” Tunneling between Tori and the Splitting of Eigenvalues of the Laplace–Beltrami Operator on Liouville Surfaces [DOI]
- 15 Vacuum Energy of the Laplacian on the Spheres [DOI]
- 16 GENERIC SIMPLICITY OF EIGENVALUES FOR A DIRICHLET PROBLEM OF THE BILAPLACIAN OPERATOR
- 17 Small volume expansion of the splitting of multiple Neumann Laplacian eigenvalues due to a grounded inclusion in two dimensions [DOI]
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