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On the basis of Buimistrov-Pekar method the polaron energy spectrum is studied in a spherical quantum dot of a polar semiconductor. The polaron correction for the ground and first excited states of the electron, depending on the size of the quantum dot is found. It is shown that refined approximation of the wave function of phonons leads to a more accurate estimation of energy polaron states and found energy levels better controlled quantum dot size than other approximations.

The Energy Levels of an Polaron in Parabolic potential well