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

Generic directness of range of the Schrödinger-type manipulator, H = Δ + V, is examined in this place study. Here, Δ is the standard Laplace controller on n-spatial part torus and V is the distress potential. On the n-spatial torus, we secondhand Rayleigh- Schrödinger perturbation hypothesis to analyse the dividing behaviour of the range on account of small distress. We confirmed the life of a distress potential V that guarantees the clarity of the range of the Schrödinger-type driver Δ+V on the n-torus in the beginning order.

Author(s) Details:

Louis Omenyi,
Department of Mathematics and Statistics, Alex Ekwueme Federal University, Ndufu-Alike, Nigeria.

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Keywords: Laplacian, schrödinger operator, spectrum, simplicity, n-torus, Rayleigh-Schrödinger perturbation

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