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PreprintCC BY 4.0arXiv

Perturbative results for fractional quantum mechanics

  • Claude Semay
  • Clara Tourbez
  • Loïc Keszeli
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Abstract

The fractional Schrödinger equation is studied with a kinetic energy that slightly deviates from the usual nonrelativistic form. The harmonic oscillator and the Kepler problem are both treated in the context of small perturbations. The usual perturbation theory is used and compared with the envelope theory. The corrections to the unperturbed Hamiltonians are analytical. The bounds computed with the envelope theory are good for the harmonic oscillator but poorer for the Kepler problem.

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Cite

BibTeXRIS
BibTeX
@misc{semay2026perturbative,
  title = {{Perturbative results for fractional quantum mechanics}},
  author = {Claude Semay and Clara Tourbez and Loïc Keszeli},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.03226},
  eprint = {2606.03226},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.03226},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Perturbative results for fractional quantum mechanics
AU  - Claude Semay
AU  - Clara Tourbez
AU  - Loïc Keszeli
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2606.03226
UR  - https://arxiv.org/abs/2606.03226
AB  - The fractional Schrödinger equation is studied with a kinetic energy that slightly deviates from the usual nonrelativistic form. The harmonic oscillator and the Kepler problem are both treated in the context of small perturbations. The usual perturbation theory is used and compared with the envelope theory. The corrections to the unperturbed Hamiltonians are analytical. The bounds computed with the envelope theory are good for the harmonic oscillator but poorer for the Kepler problem.
ER  -