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.
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