Quantum Potentials with q-Gaussian Ground States
arXiv:1011.3459
Abstract
We determine families of spherically symmetrical -dimensional quantum potential functions having ground state wavefunctions that exhibit, either in configuration or in momentum space, the form of an isotropic -Gaussian. These wavefunctions admit a maximum entropy description in terms of power-law entropies. We show that the potentials with a ground state of the -Gaussian form in momentum space admit the Coulomb potential as a particular instance. Furthermore, all these potentials behave asymptotically as the Coulomb potential for large for all values of the parameter such that
submitted