The ratio between the confinement lengths in the $xy$-plane and the $z$ direction plays an important role in determining the properties of anisotropic quantum dot. Within a variational approach of Pekar type, we investigated theoretically the effects of electric field and temperature on the ground-state binding energies of hydrogenic impurity polarons in KBr anisotropic quantum dot. The obtained results illustrate that the binding energies increase with the electric field strength and temperature but decrease with the position of the impurity when considering different confinement lengths in the $xy$-plane and the $z$ direction and present the properties of the anisotropic quantum dot.

The influence of magnetic field and Coulomb field on the Rashba spin–orbit interaction in a triangular quantum well was studied using Pekar variational method. We theoretically derived the expression of the boundmagnetopolaron ground-state energy. The energy of the bound magnetopolaron splits under the influence of the Rashba effect. From this phenomenon, it is concluded that the effects of orbital and spin interactions on the polaron energy in different directions must be considered. Because of the contribution of the magnetic field cyclotron resonance frequency to the Rashba spin–orbit splitting, the energy spacing becomes larger as the magnetic field cyclotron resonance frequency increases. Compared to the bare electron, the bound polaron is more stable, and the energy of bound polaron split is more stable.