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- W1645607513 abstract "Let M be a compact, connected C 1 manifold with a C 1 Riemannian metric or let M = R n with Euclidean metric. Let g denote the metric. On M consider the 2 2s ystem of Schr¨ odinger operators P = h 2 Δ +V +h 2 W ;V = v1 0 0 v2 ; where v1;v2 2 C 1 (M) are non-negative, andW is a C 1 , first order formally selfadjoint differential operator with real coefficients. We study the eigenfunctions of P corresponding to the lowest eigenvalues in the semi-classical limit h! 0. They are concentrated near a minimal geodesic with respect to the Agmon metric vg, v = min(v1;v2), connecting two non-degenerate zeros of v (wells). This metric is Lipschitz continuous but not C 2 at = fx 2 M; v1(x )= v2(x)g. When the derivative of v1 v2 along does not vanish on and the intersection is transversal we obtain WKB expansions of the eigenfunctions. At they are expressed in terms of derivatives Yk; =@ k Y=@ k of suitable parabolic cylinder functions Y. As an application of the WKB constructions we compute the splitting due to tunnelling of the lowest eigenvalues of P under a strong symmetry condition." @default.
- W1645607513 created "2016-06-24" @default.
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- W1645607513 date "1997-01-01" @default.
- W1645607513 modified "2023-09-24" @default.
- W1645607513 title "WKB expansions for systems of Schrödinger operators with crossing eigenvalues" @default.
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- W1645607513 doi "https://doi.org/10.3233/asy-1997-14101" @default.
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