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Conformally flat Riemannian metrics, Schrödinger operators, and semiclassical approximation. (English) Zbl 0616.34020

Authors’ summary: ”A relationship between Laplace-Beltrami and Schrödinger operators on Euclidean domains is analyzed and exploited for several purposes: We use the Schrödinger equation to analyze the spectra of Laplace-Beltrami operators with periodic metrics on \(R^ v\), and use geometric notions and nonlinear differential equations to bound spectra and Green functions of Schrödinger operators in various ways. We also have a new, more operator-theoretic analysis of the semiclassical limit and the Liouville-Green (or JWKB) approximation in one dimension.”
Reviewer: P.N.Bajaj

MSC:

34L99 Ordinary differential operators
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