Hydrogen atom in momentum space with a minimal length
arXiv:1009.0935 · doi:10.1103/PhysRevA.82.022105
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.
10 pages
References in corpus (4)
- Hydrogen-atom spectrum under a minimal-length hypothesis
- Minimal Length Uncertainty Relation and gravitational quantum well
- Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
- Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background