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The effect of the confined LO‐phonon on the impurity binding energy in a CdSe quantum dot has been calculated by using a variational approach. The charge carrier (electron and ion)–phonon coupling is treated within the adiabatic approximation. The results show that this effect decreases as the dot size increases and depends on the impurity position. The confined LO‐phonon effect decreases as the impurity is displaced from the center to the dot boundary.

The binding energy of an exciton in a cubic quantum dot has been calculated with and without including the electron (hole)-confined longitudinal optical phonon interactions, using a variational approach and within the effective mass approximation. The quantum confinement effect is described by an infinitely deep well in the envelope-function approximation. The charge carrier phonon coupling is treated within the adiabatic approximation. As the dot size increases, the results show that the contribution of the confined longitudinal optical phonon on the binding energy decreases and the correction to the excitonic state increases.

The properties of polarons and bipolarons are studied by the variational method taking into account the density of state for Van Hove singularity (V.H.S) in two-dimension (2D) in the presence of a perpendicular magnetic field. It should be noticed that the bipolaron stability region is relatively sensitive to the application of a magnetic field. In 2D, for ω c =0.8 the value of α c =1 is compared to α c =1.6 for ω c =0.