Study of oscillator strengths of hydrogenic impurity in a inhomogeneous finite and infinite spherical quantum dots

In this study, using the effective mass approximation and continuum dielectric media, the Schrödinger equation of nano systems is solved in terms of Whittaker functions. The oscillator strengths of both finite and infinite confining potentials from ground to the first and second allowed excited states are calculated with hydrogenic impurity. Regarding this, the oscillator strengths of system with hydrogenic impurity are studied by means of dipole approximation. The results show that in the case of constant shell thickness, when the inner radius of shell thickness is small, the value of oscillator strengths of both transitions (from ground to the first and second allowed excited states) is strongly affected by changes in shell thickness. In the large enough inner radius of shell thickness, the corresponding oscillator strength curves coincide for two transitions. Generally, these two transitions behave differently, i.e. by increasing the value of inner radius of shell, the first two transitions decrease and decrease respectively (due to conservation of probability).