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Research Article Open access CC BY 4.0

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/2017/31160

Abstract

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.

Laplacian Schrödinger operator spectrum simplicity n-torus Rayleigh-Schrödinger perturbation.

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