Corpus ID: 218971645

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

  title={The Breit-Wigner series for noncompactly supported potentials on the line},
  author={Aidan Backus},
  journal={arXiv: Analysis of PDEs},
  • 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
  • Bachelor’s thesis. UC Berkeley,
  • 2020
A conjecture on the resonances of a non-compactly supported potential". Bachelor's thesis
  • 2020