Generic Simplicity of the Spectrum of a Schrödinger-type Operator on a Riemannian Manifold

Omenyi, Louis (2023) Generic Simplicity of the Spectrum of a Schrödinger-type Operator on a Riemannian Manifold. In: Research Highlights in Mathematics and Computer Science Vol. 4. B P International, pp. 99-121. ISBN 978-81-961092-4-0

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Abstract

Generic simplicity of spectrum of the Schrödinger-type operator, H = + V, is investigated in this study. Here, is the standard Laplace operator on n-dimensional unit torus and V is the perturbation potential. On the n-dimensional torus, we used Rayleigh- Schrödinger perturbation theory to analyse the splitting behaviour of the spectrum due to infinitesimal perturbation. We proved the existence of a perturbation potential V which guarantees the simplicity of the spectrum of the Schrödinger-type operator +V on the n-torus at first order.

Item Type: Book Section
Subjects: Open Research Librarians > Computer Science
Depositing User: Unnamed user with email support@open.researchlibrarians.com
Date Deposited: 04 Oct 2023 05:29
Last Modified: 04 Oct 2023 05:29
URI: http://stm.e4journal.com/id/eprint/1614

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