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arXiv · 2005.13765

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

Aidan Backus
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Abstract

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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Aidan Backus. 2020-05-28. The Breit-Wigner series for noncompactly supported potentials on the line. https://arxiv.org/abs/2005.13765

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