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Extended Results on Absorbing Boundary Conditions as Limits of Complex Potentials

  • Rashi Kaimal
  • Roderich Tumulka
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Abstract

In quantum mechanics, among the proposals for how to compute the probability distribution of detection time and place along a given spatial surface or in a given volume, two leading candidates involve absorbing boundary conditions (ABCs) and complex absorbing potentials (CAPs) for the Schrödinger equation. Here, we extend earlier results on how the two are related. It was previously shown that ABCs arise as a limiting case of CAPs, but for that a (reflecting) Neumann boundary condition was assumed at the end of the region with the CAP. Here, we obtain ABCs in a different limit using a Dirichlet boundary condition at the end of the CAP region, which seems more practically relevant and realizable.

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Cite

BibTeXRIS
BibTeX
@misc{kaimal2026extended,
  title = {{Extended Results on Absorbing Boundary Conditions as Limits of Complex Potentials}},
  author = {Rashi Kaimal and Roderich Tumulka},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11865},
  eprint = {2610.11865},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11865},
}
RIS
TY  - UNPB
TI  - Extended Results on Absorbing Boundary Conditions as Limits of Complex Potentials
AU  - Rashi Kaimal
AU  - Roderich Tumulka
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11865
UR  - https://arxiv.org/abs/2610.11865
AB  - In quantum mechanics, among the proposals for how to compute the probability distribution of detection time and place along a given spatial surface or in a given volume, two leading candidates involve absorbing boundary conditions (ABCs) and complex absorbing potentials (CAPs) for the Schrödinger equation. Here, we extend earlier results on how the two are related. It was previously shown that ABCs arise as a limiting case of CAPs, but for that a (reflecting) Neumann boundary condition was assumed at the end of the region with the CAP. Here, we obtain ABCs in a different limit using a Dirichlet boundary condition at the end of the CAP region, which seems more practically relevant and realizable.
ER  -