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PreprintarXiv licencearXiv

Norm of resonance states in quantum scattering and electromagnetic systems

  • Florian Lorenz
  • Jan Möseritz-Schmidt
  • Roland Ketzmerick
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Abstract

Resonance states spatially diverge and are thus not square integrable. Instead, their norm is defined by the biorthogonal scalar product of left and right states. We replace the corresponding volume integral over infinite space by a convenient boundary integral in piecewise-homogeneous systems and apply this procedure to diverse physical settings. For a quantum particle in any number of dimensions we treat hard-wall and piecewise-constant potentials. For electromagnetic systems with piecewise-homogeneous material properties, we consider three-dimensional and effectively two-dimensional cavities.

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Cite

BibTeXRIS
BibTeX
@misc{lorenz2026norm,
  title = {{Norm of resonance states in quantum scattering and electromagnetic systems}},
  author = {Florian Lorenz and Jan Möseritz-Schmidt and Roland Ketzmerick},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.22052},
  eprint = {2607.22052},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.22052},
}
RIS
TY  - UNPB
TI  - Norm of resonance states in quantum scattering and electromagnetic systems
AU  - Florian Lorenz
AU  - Jan Möseritz-Schmidt
AU  - Roland Ketzmerick
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2607.22052
UR  - https://arxiv.org/abs/2607.22052
AB  - Resonance states spatially diverge and are thus not square integrable. Instead, their norm is defined by the biorthogonal scalar product of left and right states. We replace the corresponding volume integral over infinite space by a convenient boundary integral in piecewise-homogeneous systems and apply this procedure to diverse physical settings. For a quantum particle in any number of dimensions we treat hard-wall and piecewise-constant potentials. For electromagnetic systems with piecewise-homogeneous material properties, we consider three-dimensional and effectively two-dimensional cavities.
ER  -