# Resonance free domain for Schr\\"odinger operators with repulsive potential

Source: [Resonance free domain for Schr\\"odinger operators with repulsive potential](<https://www.sota2.com/research/paper/68fa45921e209131ce919a84>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T05:21:48.207Z

Authors: K. Itakura

Published: 2023-04-12T02:11:10.000Z

## Abstract

We study resonances for the Schr\\"odinger operators with quadratic or sub-quadratic repulsive potential. In the present paper, we show the non-existence of resonances in some complex neighborhood of a fixed energy by employing schemes of Briet-Combes-Duclos and Hunziker and by introducing a proper distortion based on, but slightly modified, positive commutator method of Mourre.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2304.05569>)

[PDF](<https://arxiv.org/pdf/2304.05569.pdf>)