Some Aspects of Theory of Schrödinger Operators on Riemannian Manifold - Diyab, Farah; Reddy, B. Surender (Communications in Mathematics and Applications, 2022)
This paper deals with a given Riemannian manifold \(\mathcal{M}\). One of the main tasks is description of spectrum of several classes of Schrödinger operator \(P=\frac{-h^{2}}{2}Δ _{g}+V\) where \(Δ _{g}\) is Laplace Beltrami operator and \(V\) is potential on manifold. We illustrate the inverse and direct problems of \(Δ _{g}\) and the way to discover the geometry of Riemannian manifold from spectral data.