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Conformally flat Riemannian metrics, Schrödinger operators, and semiclassical approximation

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
66
Issue
2
Identifiers
DOI: 10.1016/0022-0396(87)90030-1
Disciplines
  • Mathematics

Abstract

Abstract 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.

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