Corpus ID: 218971645

# The Breit-Wigner series for noncompactly supported potentials on the line

@article{Backus2020TheBS,
title={The Breit-Wigner series for noncompactly supported potentials on the line},
author={Aidan Backus},
journal={arXiv: Analysis of PDEs},
year={2020}
}
• Aidan Backus
• Published 28 May 2020
• Physics, Mathematics
• arXiv: Analysis of PDEs
We propose a conjecture stating that for resonances, $\lambda_j$, of a noncompactly supported potential, the series $\sum_j \operatorname{Im} \lambda_j/|\lambda_j|^2$ diverges. This series appears in the Breit-Wigner approximation for a compactly supported potential, in which case it converges. We provide heuristic motivation for this conjecture and prove it in several cases.

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A conjecture on the resonances of a non-compactly supported potential
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A conjecture on the resonances of a non-compactly supported potential". Bachelor's thesis
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