Hydrogen atom in momentum space with a minimal length

Details Hydrogen atom in momentum space with a minimal length Hydrogen atom in momentum space with a minimal length

2010-09-05

arxiv.org/abs/1009.0935v1

Phys.Rev.A82:022105,2010

Physics

Quantum Physics

10 pages

Scientific paper

10.1103/PhysRevA.82.022105

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

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