Some Aspects of Theory of Schrödinger Operators on Riemannian Manifold
DOI:
https://doi.org/10.26713/cma.v13i5.2258Keywords:
Manifolds, Spectral theory, Laplacian, Spectral geometryAbstract
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 \(P=\frac{-h^{2}}{2}\Delta _{g}+V\) where \(\Delta _{g}\) is Laplace Beltrami operator and \(V\) is potential on manifold. We illustrate the inverse and direct problems of \(\Delta _{g}\) and the way to discover the geometry of Riemannian manifold from spectral data.
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