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Within the effective mass approximation an adiabatic description of spheroidal and dumbbell quantum dot models in the regime of strong dimensional quantization is presented using the expansion of the wave function in appropriate sets of single-parameter basis functions. The comparison is given and the peculiarities are considered for spectral and optical characteristics of the models with axially symmetric confining potentials depending on their geometric size making use of the total sets of exact and adiabatic quantum numbers in appropriate analytic approximations

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In this article, we investigate an exactly solvable model, describing the behavior of electrons in a cylindrical quantum dot GaAs / Ga 1-x Al x As with parabolic confinement potential under the influence of external electrical and magnetic fields, directed along the axes of the cylinder. The wave-function and energy levels of the electron are found. An exact analytical expression for the energy of Stark shift is obtained. It has been shown that only the quadratic Stark effect takes place in the considered system. On the basis of the obtained results, the coefficient of direct interband transition in the system is calculated.

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