Generalized coherent states for the d-dimensional Coulomb problem

In this paper a set of generalized coherent states for the d-dimensional Coulomb problem in coordinate representation are constructed. A coordinate transformation in hyperspherical space is used that maps the d-dimensional Coulomb problem into the D-dimensional harmonic oscillator and the generalized coherent states for the d-dimensional Coulomb problem are then obtained. This exactly soluble model can provide an adequate means for a quantum coherency description of the Coulomb problem in arbitrary dimensions, specifically in the special case of the hydrogen atom, in many theoretical and applied related fields such as in coherent scattering.