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Der AHP-Preis 2015 wurde an Ira Herbst und Juliane Rama für ihre Arbeit

"Instability for Pre-existing Resonances under a small constant Electric Field"

verliehen. (Dieser Preis wird jedes Jahr für den bemerkenswertesten Artikel in der Zeitschrift Annales Henri Poincaré verliehen.)

# Asymptotic Eigenfunctions for Schrödinger operators on a vector bundle

#### Autoren: Matthias Ludewig, Elke Rosenberger (2020)

In the limit $$\hbar \to 0$$, we analyze a class of Schrödinger operators $$H_\hbar = \hbar^2 L + \hbar W + V\cdot id_{\mathscr{E}}$$ acting on sections of a vector bundle $$\mathscr{E}$$ over a Riemannian manifold $$M$$ where $$L$$ is a Laplace type operator, $$W$$ is an endomorphism field and the potential energy $$V$$ has a non-degenerate minimum at some point $$p\in M$$. We construct quasimodes of WKB-type near $$p$$ for eigenfunctions associated with the low-lying eigenvalues of $$H_\hbar$$. These are obtained from eigenfunctions of the associated harmonic oscillator $$H_{p,\hbar}$$ at $$p$$, acting on smooth functions on the tangent space.

Zeitschrift:
Reviews in Mathematical Physics
Verlag:
World Scientific

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