# Agmon-type decay of eigenfunctions for a class of Schr\"{o}dinger operators with non-compact classically allowed region

@inproceedings{Marx2021AgmontypeDO, title={Agmon-type decay of eigenfunctions for a class of Schr\"\{o\}dinger operators with non-compact classically allowed region}, author={Christoph A. Marx and Hengrui Zhu}, year={2021} }

An important result by Agmon implies that an eigenfunction of a Schrödinger operator in Rn with eigenvalue E below the bottom of the essential spectrum decays exponentially if the associated classically allowed region tx P Rn : V pxq ď Eu is compact. We extend this result to a class of Schrödinger operators with eigenvalues, for which the classically allowed region is not necessarily compactly supported: We show that integrability of the characteristic function of the classically allowed region…

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