The electronic structure of a hydrogenic impurity atom located at the center of a multilayer coated quantum dot (CQD) is investigated. The electronic eigenstates of the CQD system are expressed in terms of the geometry and the material parameters by solving the Schrodinger equations analytically. Image potential effects are ignored and the effective mass approximation is employed. The ground state energy is found to be strongly influenced by the shell thickness and confined potential. In contrast to previous work, our eigenfunctions are expressed in terms of the Whittaker functions in any region, no matter where the energy levels are, i.e., whether they are higher or lower than the potential barriers. Our approach is simpler and has general significance, e.g., the bound state eigenenergies of any n-layered quantum dot can be easily determined by directly solving just "one"(2n-2)-rank secular determinant equation instead of solving 2~(n) equations. One can also easily and quickly determine whether a system has bound states by using the Whittaker function approach.
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