Effect of electron-phonon interaction on the energy spectrum of a quantum antidot in the presence of a uniform strong magnetic field

We have studied the effect of electron-phonon interaction for small electron-phonon coupling on the electronic energy spectrum of an electron confined by a parabolic potential and a repulsive antidot potential in the presence of a uniform strong magnetic field and an Aharonov-Bohm flux field by using a variational procedure. We have shown that the presence of the antidot potential removes degeneracy of the Landau levels and electron-phonon interaction has nonnegligible effects on these levels.