Quantum potentials with -Gaussian ground states

We determine families of spherically symmetrical D -dimensional quantum potential functions V ( r ) having ground-state wavefunctions that exhibit, either in configuration space or in momentum space, the form of an isotropic q -Gaussian. These wavefunctions admit a maximum-entropy description in terms of S q power-law entropies. We show that the potentials with a ground state of the q -Gaussian form in momentum space admit the Coulomb potential − 1 / r as a particular instance. Furthermore, all these potentials behave asymptotically as the Coulomb potential for large r for all values of the parameter q such that 0 < q < 1 .