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arXiv · 1009.0935

Hydrogen atom in momentum space with a minimal length

Djamil Bouaziz·Nourredine Ferkous
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Abstract

A momentum representation treatment of the hydrogen atom problem with a generalized uncertainty relation,which leads to a minimal length (ΔX_{i})_{min}= \hbar \sqrt(3β+β'), is presented. We show that the distance squared operator can be factorized in the case β'=2β. We analytically solve the s-wave bound-state equation. The leading correction to the energy spectrum caused by the minimal length depends on \sqrtβ. An upper bound for the minimal length is found to be about 10^{-9} fm.

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Djamil Bouaziz, Nourredine Ferkous. 2010-09-05. Hydrogen atom in momentum space with a minimal length. https://doi.org/10.1103/physreva.82.022105

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