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Time-Dependent Density Functional Theory with Coulomb Interactions

  • Asbjørn Bækgaard Lauritsen
  • Mathieu Lewin
  • Jakob Oldenburg
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Abstract

We provide the first fully rigorous justification of time-dependent density functional theory in the continuum: Given a time-dependent density, we prove that there exists an external potential, unique up to a time-dependent constant, such that the corresponding Schrödinger equation reproduces the given density. This potential can be obtained with an iteration scheme. Our argument covers Coulomb interactions and does not need any Taylor expansion in time. It instead requires analyticity in space for the density and potential, which is compatible with extended nuclei.

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Cite

BibTeXRIS
BibTeX
@misc{lauritsen2026timedependent,
  title = {{Time-Dependent Density Functional Theory with Coulomb Interactions}},
  author = {Asbjørn Bækgaard Lauritsen and Mathieu Lewin and Jakob Oldenburg},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08983},
  eprint = {2609.08983},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05744842v1},
}
RIS
TY  - UNPB
TI  - Time-Dependent Density Functional Theory with Coulomb Interactions
AU  - Asbjørn Bækgaard Lauritsen
AU  - Mathieu Lewin
AU  - Jakob Oldenburg
PY  - 2026
DA  - 2026/09/08
PB  - HAL
DO  - 10.48550/arxiv.2609.08983
UR  - https://hal.science/hal-05744842v1
AB  - We provide the first fully rigorous justification of time-dependent density functional theory in the continuum: Given a time-dependent density, we prove that there exists an external potential, unique up to a time-dependent constant, such that the corresponding Schrödinger equation reproduces the given density. This potential can be obtained with an iteration scheme. Our argument covers Coulomb interactions and does not need any Taylor expansion in time. It instead requires analyticity in space for the density and potential, which is compatible with extended nuclei.
ER  -