Hydrogen atom in momentum space with a minimal length

Understand

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}.