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Asian Research Journal of Mathematics

Asian Research Journal of Mathematics, 2456-477X,Vol.: 2, Issue.: 1


Generic Simplicity of a Schrödinger-type Operator on the Torus


Louis Omenyi1*, Emmanuel Nwaeze1 and McSylvester Omaba1

1Department of Mathematics, Computer Science, Statistics and Informatics, Federal University, Ndufu-Alike, Ikwo, Nigeria.


Article Information
(1) Dijana Mosic, Department of Mathematics, University of Nis, Serbia.
(1) Golam Hafez, Chittagong University of Engineering and Technology, Chittagong-4349, Bangladesh.
(2) Horácio Santana Vieira, Universidade Federal da Paraíba, Brazil and Universidade Estadual da Paraíba, CEP, Brazil.
Complete Peer review History: http://www.sciencedomain.org/review-history/17499




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.


Keywords :

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


Full Article - PDF    Page 1-19    Article Metrics


DOI : 10.9734/ARJOM/2017/31160

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