Few-Body Syst DOI 10.1007/s00601-016-1110-4 M. C. Onyeaju · J. O. A. Idiodi · A. N. Ikot · M. Solaimani · H. Hassanabadi Linear and Nonlinear Optical Properties in Spherical Quantum Dots: Generalized Hulthén Potential Received: 2 March 2016 / Accepted: 13 April 2016 © Springer-Verlag Wien 2016 Abstract In this work, we studied the optical properties of spherical quantum dots confined in Hulthén potential with the appropriate centrifugal term included. The approximate solution of the bound state and wave functions were obtained from the Schrödinger wave equation by applying the factorization method. Also, we have used the density matrix formalism to investigate the linear and third-order nonlinear absorption coefficient and refractive index changes. 1 Introduction Semiconductor quantum dots (QDs) have attracted interest in recent years from experimentalist and theorist. The interest generated from QDs is as a result of the advances made in the growth and processing of heterostruc- tures [1, 2] in which both electrons and valence holes can be confined in all three dimensions. This progress in growth is coupled with progress in “single dot spectroscopy”, where individual QDs can be investigated or interrogated optically [3–11] and other reference therein. The studies on these structures open a new field in physics and engineering, and also offers a wide range of applications for optoelectronic devices, high perfor- mance laser, optical sources, and detectors [12–16]. QDs are particularly significant for optical applications due to their high extinction coefficient and narrow or symmetric emission spectra. They offer extra degrees of freedom in the design of semiconductor junction devices, because both the impurity doping and the conduction and valence band offsets at the junction can be controlled [17]. It is therefore necessary to relate different optical spectroscopies to the electronic properties of QDs since the electronic properties control all other properties within the dot. Hence the analytical solution of the bound state energy with the appropriate approximation for the generalized Hulthén potential is considered in this present study. Several researchers have investigated the electronic and optical properties of low dimensional QDs with various potential models such as Coulomb, Rosen-Morese, Poschl-Teller, Tietz, Woods-Saxon, and Eckart potential [18–24]. More importantly, Ref. [18– 20] studied these effects by using Coulomb potential. For example, Kasapoglu et al. [18] studied the effect of hydrostatic pressure on optical transitions in quantum-well using Coulomb potential model while Kazaryan et M. C. Onyeaju (B ) · A. N. Ikot Theoretical Physics Group, Department of Physics, University of Port Harcourt, P.M.B. 5323, Choba Port Harcourt, Nigeria E-mail: michael.onyeaju@uniport.edu.ng J. O. A. Idiodi Department of Physics, University of Benin, Benin City, Edo State, Nigeria M. Solaimani Department of Physics, Faculty of science, Qom University of Technology, Qom, Iran H. Hassanabadi Physics Department, Shahrood University of Technology, Shahrood, Iran