Department for Theoretical Physics,

Ivan Franko Lviv National University,

12 Drahomanov Str.,

Lviv, UA-79005,

UKRAINE

E-mail: fityo@ktf.franko.lviv.ua, tkachuk@ktf.franko.lviv.ua, chair@KTF.Franko.Lviv.UA

**1D Coulomb problem with deformed Heisenberg algebra**

**Abstract:**

We have found exact energy spectrum and corresponding have function
in momentum representation for 1 dimensional Coulomb problem with the following
deformed commutation relation: $[X,P]=i(1+\beta P^2)$. This deformation
leads to the existence of a finite lower bound to the possible resolution
of length.