Asymptotic eigenfunctions for Schrödinger operators on a vector bundle
Keyword(s):
In the limit [Formula: see text], we analyze a class of Schrödinger operators [Formula: see text] acting on sections of a vector bundle [Formula: see text] over a Riemannian manifold [Formula: see text] where [Formula: see text] is a Laplace type operator, [Formula: see text] is an endomorphism field and the potential energy [Formula: see text] has a non-degenerate minimum at some point [Formula: see text]. We construct quasimodes of WKB-type near [Formula: see text] for eigenfunctions associated with the low-lying eigenvalues of [Formula: see text]. These are obtained from eigenfunctions of the associated harmonic oscillator [Formula: see text] at [Formula: see text], acting on smooth functions on the tangent space.
2013 ◽
Vol 39
(1)
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pp. 1-33
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2017 ◽
pp. 87-116
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2005 ◽
Vol 02
(04)
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pp. 543-552
Keyword(s):