The non-relativistic dipole transition matrix elements, oscillator strengths, transition probabilities and lifetimes of the ground and lowest excited states of the centered and off-centered confined Hydrogen atom in a spherical cavity, were investigated via a variational method using B-splines as basis functions. These atomic parameters, obtained with a high accuracy, were found to be strongly affected by the off-center displacement which induces the increase of the splitting between initially m's degenerate states. Due to the displacement of the atom from the center, some transitions that were initially forbidden have non-zero probabilities. The results obtained for the 2sσ, 2pσ, 2pπ, 3dσ, 3dπ, and 3dδ states have shown that, with the increase of the displacement, the state lifetimes exhibit one or several extrema depending on the confinement radius and the magnetic quantum number.

Nonrelativistic dipole matrix elements, oscillator strengths, transition probabilities and states lifetimes of quantum dots with centered and off-centered hydrogenic impurities are studied. The effects of the off-center displacement combined to the shape of the confining potential are investigated. These optical parameters are found to be strongly modified by the parameters characterizing the confinement as well as by taking into account of the off-center shift. It is found that the oscillator strengths present a minimum for certain values of the confinement potential range and of the off-center displacement, principally due to the reaching of a low energy gap between the levels involved in the concerned transition. Likewise, the states lifetimes increase with the off-center displacement whatever the shape of the confinement potential is because of the reduction of the gap between the energies of the states when the displacement is no longer equal to zero.

Non-relativistic energy levels, binding energies and oscillator strengths of CdSe⁄ZnT e core/shell spherical quantum dots with or without impurities submitted to an external magnetic field have been investigated by using a B-spline based variational method, within the framework of the effective mass approximation. In the case where the system contains hydrogenic impurity, the effects of its off-center displacement combined to the height of the confining potential have also been studied. The dielectric constant as well as the effective mass are considered to be dependent on the radius. The modifications occurring due to the presence of the magnetic field have been analyzed. We have found that the electronic and optical properties are strongly affected by the magnetic field strength, the spatial confinement and the off-center displacement. The oscillator strengths and the binding energies increase with the magnetic field, but its effect on the binding energies (both ground and excited states) is dimmed by the reduction of the core-to-shell radii ratio and the increase of the off-center displacement to the vicinity of the shell. However, the oscillator strengths increase with the magnetic field when the off-center displacement increases towards the shell.

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