Taras FITYO, Volodymyr TKACHUK and Ivan VAKARCHUK
Department for Theoretical Physics,
Ivan Franko Lviv National University,
12 Drahomanov Str.,
Lviv, UA-79005,
E-mail: fityo@ktf.franko.lviv.ua, tkachuk@ktf.franko.lviv.ua, chair@KTF.Franko.Lviv.UA

1D Coulomb problem with deformed Heisenberg algebra

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.