Polaron in cylindrical and spherical quantum dots

Polaron states in cylindrical and spherical quantum dots with parabolic confinement potentials are investigated applying the Feynman variational principle. It is observed that for both kinds of quantum dots the polaron energy and mass increase with the increase of Fr"{o}hlich electron-phonon coupling constant and confinement frequency. In the case of a spherical quantum dot, the polaron energy for the strong coupling is found to be greater than that of a cylindrical quantum dot. The energy and mass are found to be monotonically increasing functions of the coupling constant and the confinement frequency