In this study, the energy levels of spherical quantum dot (QD) and spherical quantum anti-dot (QAD) with hydrogenic impurity in the center, in the presence of spin-orbit interaction (SOI) and weak external magnetic field have been studied. To this aim, solving the Schrodinger equation for the discussed systems by using the finite difference method, the wave functions and energies of these systems are calculated. Then the effect of the external magnetic field, system radius size and height of potential barrier on the energy levels and also the linear, nonlinear and total absorption coefficients, (ACs), of the mentioned systems are studied. Numerical results show that the SOI in both models causes a split of 2p level into two sub-levels of 2p_(1/2)and 2p_(3/2) where the low index indicates the total angular momentum J. Also, considering the electron spin, under an applied magnetic field, the 1s and 2p levels split into two sub-levels and six sub-levels, respectively. Furthermore, in this research, it is proved that energy changes are significantly different as a function of radius size and height of the potential barrier in QD and QAD models and the ACs of these systems behave differently according to the incident photon energy at the same condition. Manuscript profile

In this work, the effect of magnetic field on
electronic spectra and absorption coefficient of 𝐺𝑎𝐴𝑠/
𝐺𝑎1−𝑥 𝐴𝑙𝑥𝐴𝑠 spherical quantum dot (QD) and
𝐺𝑎1−𝑥 𝐴𝑙𝑥𝐴𝑠/𝐺𝑎𝐴𝑠 spherical quantum anti-dot (QAD)
with hydrogenic impurity are reported both theoretically
and numerically. The theoretical results which are
obtained based on perturbation theory are in agreement
with numerical results, which are obtained by using the
finite difference method. Using numerical solutions,
energy eigenvalues and eigenfunctions of the Schrödinger
equation in these structures are obtained. The effects of
the magnetic field on1s→2p0 absorption coefficient and
also on 1s and 2p energy levels of the QD and the QAD
have been investigated. The wave functions and energies
of an electron in these spherical systems, have been
studied. The results clearly show that the energy levels
changes and absorption coefficients in the QD and QAD
models are significantly different. It is also observed
some new degeneracies are appeared in the QAD model
under the applied magnetic field. Manuscript profile