Excitonic eigenfunctions in a fractional dimensional space

The binding energies in quantum wires and dots have recently been calculated by solving both the Poisson and the Schrödinger equations in the fractional dimension spaces proposed by Stillinger. By a Fourier analysis of the non-Coulombic potential that is used it is shown in the present paper that the ‘dimension’ parameters associated with each equation should be the same. The eigenfunctions are also calculated. It is shown, in particular cases, that they coincide with those obtained by other authors and different models. The difference it makes to use a potential from the Poisson equation instead of the Coulombic one is also made evident.