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Spectral geometry: Two exactly solvable models. (English) Zbl 0959.58501

Summary: Two exactly solvable models illustrating the links between spectral properties of Hamiltonians, connections on the induced Hilbert bundles and topological characteristics of the basis spaces are considered. The first of them is based on the extension theory for symmetric operators and the second on the one-dimensional Laplace operator with parametrical boundary conditions.

MSC:

58J90 Applications of PDEs on manifolds
46N50 Applications of functional analysis in quantum physics
47N50 Applications of operator theory in the physical sciences
58Z05 Applications of global analysis to the sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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