Analytic calculation for the binding energy of an on-center donor impurity in core/shell/shell quantum dot

In this study, we present a general analytic solution for any system describing a Core/Shell/Shell Quantum Dot or briefly CSSQD with and without an on-center donor impurity using only one solution wave function build by a linear combination of the Whittaker functions. In the framework of the effective mass approximation, in the conduction band, we apply this general solution wave function on a special case, ZnS/HgS/ZnS multi-shell quantum dot in order to calculate the confinement energy and binding energy for the ground state and several other excited state as well as the probability densities, the results show that the general solution does matches with the reference solutions given by the spherical Bessel function for the impurity-less case, and agrees with the results when the energy is positive when the impurity is present, which are given by the coulomb functions.