Analytical expressions for the linear and nonlinear optical susceptibilities of spherical quantum dots are obtained using the Schrödinger equation. To solve the Schrödinger equation, the Nikiforov-Uvarov method was used, assuming that electrons isolated in the medium are associated with the Gelman inverse quadratic potential. Using the density matrix formalism, analytical expressions were obtained for the coefficients of linear and nonlinear absorption and changes in the refractive index of quantum dots. Elements of the matrix of the electric dipole moment l=± 1 and m = 0 are obtained according to the selection rules. To demonstrate the results obtained, we used the real physical characteristics of quantum dots obtained from gallium arsenide (GaAs).
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Qoraboyev, Kamoliddin and Sapayev, Usmon
"Theoretical study of the mechanisms of absorption of semiconductor spherical quantum dots in the framework of quantum mechanics,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 5:
1, Article 6.