Confined orbitals in fullerenes and quantum dots calculated by analytic continuation method

The Schrödinger equation with a Gaussian potential to model a confined system as a quantum dot or a hydrogen atom inside a fullerene is solved by using the analytic continuation method. The use of the Rodrigues formula allows us to obtain in an easy way the coefficients of the power series expansion of the Gaussian potential in terms of the Hermite polynomials. Recurrence formulas have been obtained for the series of the states of one electron confined by that potential. This method is simpler and computationally more efficient than others employed to model quantum dots using Gaussian potentials