Coherent states for the Kepler-Coulomb problem on a sphere

An algebraic approach to Kepler problem in a curved space is introduced. By using this approach, the creation and annihilation operators associated to this system and their algebra are calculated. These operators satisfy a deformed Weyl-Heisenberg algebra which can be assumed as a deformed su(2) algebra. By using this fact, the nonlinear coherent states of this system are constructed. The scalar product and Bargmann representation of this family of nonlinear coherent states are constructed. The present contribution shows that these nonlinear coherent states possess some non-classical features which strongly depend on the Kepler coupling constant and space curvature. Depending on the non-classical measures, the smaller the curvature parameter, the more the non-classical features. Moreover, the stronger Kepler constant provides more non-classical features.