Perturbative results for fractional quantum mechanics

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.

arXiv:2606.03226 [quant-ph]

(or arXiv:2606.03226v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.03226 Focus to learn more arXiv-issued DOI via DataCite

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