Abstract
The polaronic corrections to the first excited-state energies of an electron in a parabolic quantum dot are obtained variationally for the entire range of the electron-phonon coupling constant and for arbitrary confinement length using a canonical transformation method based on the Lee-Low-Pines-Gross formalism. Simple analytical results are obtained in some interesting limiting cases and for arbitrary values of the parameters the nature of the excited state is studied numerically. The theory is applied to two- and three-dimensional GaAs quantum dots to obtain information about the existence of both the effective mass and the relaxed excited states of a polaron in these systems.
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