الفهرس 
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Abstract
The binding energy of a hydrogenic impurity in a single Spherical Quantum Dot (SQD) has been calculated by utilizing techniques that differ from those used in our earlier work. In off-central and central impurities the time independent perturbation theory has been applied in the case of parabolic confining potential. The inverse distance between the electron and the center of the impurity has been expanded as a series in Legendre Polynomials and spherical harmonics. Also, the Asymptotic Iteration Method (AIM) has been investigated with a confining potential that consists of three terms. The first term stands for the potential due to central impurity while the last term represents the parabolic potential. The (AIM) has been applied to determine the binding energy of a central impurity. This has not been done hitherto. The ground state and the first approximation agree entirely with the result of the perturbation technique while the second approximations of both methods differ by about 16.5 % which is quite reasonable.
The exact solutions of the radial Schrödinger equation have been investigated subject to specific confining potentials. The results of all earlier treatments have been modified and extended to include the second node solutions.
The case of multilayered spherical quantum dot (MSQD) in the presence of a central impurity has been explored. The confining potentials have been taken to be finite or parabolic. In the latter case an analytical approach has been utilized to obtain the solution unlike an earlier treatment (Akgül et al [4]) where an entire numerical technique has been applied. In the presence of the central impurity, the asymptotic iteration method (AIM) has been employed to obtain the solutions in the dot regions. This is one of the main aims of the thesis. In fact, the AIM has not been used before to deal with such type of problems. The results obtained for the hydrogenic binding energy in the ground state 0S (l=0) consistent to a great extent with the corresponding results of Akgül et al [4]. The calculations have confirmed strongly the importance of the AIM in solving problems of complicated potential energies.