Exact numerical solution of the lower lying state binding energies of hydrogenic impurity located at the center of a GaAs-A1xGa1-xAs quantum circle and quantum dot. The eigenfunctions of the impurity can be expressed in terms of Whittaker functions and Coulomb wave functions. The ground state and lower lying state binding energies are expressed in terms of the circle and dot radius. For the single layer quantum circle, the ground state binding energy approaches 4 Ry as the radius approaches infinite and zero, like a hydrogenic impurity in 2-D. For the single layer quantum dot, the ground state binding energy approaches 1 Ry as the radius approaches infinite and zero, like a hydrogenic impurity in 3-D. For the multi-layer case, the ground state binding energy approaches the same value as the single layer case as the radius approaches infinite, but it apporaches different value as the radius reduces to zero. Our results are in agreement with the prediction of He8.
