Generic Simplicity of the Spectrum of a Schrödinger-type Operator on a Riemannian Manifold| Chapter 7 | Research Highlights in Mathematics and Computer Science Vol. 4

 Generic directness of spectrum of the Schrödinger-type controller, H = Δ + V, is investigated in this place study. Here, Δ is the standard Laplace operator on n-spatial unit torus and V is the distress potential. On the n-dimensional torus, we secondhand Rayleigh- Schrödinger perturbation theory to analyse the dividing behaviour of the spectrum on account of infinitesimal distress. We proved the life of a perturbation potential V that guarantees the simplicity of the range of the Schrödinger-type operator 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.

Please see the link here: https://stm.bookpi.org/RHMCS-V4/article/view/9161