Path Integral Approach for Multi-dimensional Polarons in a Symmetric Quantum Dot

Within the framework of Feynman-Haken path-integral theory, the general expression of the ground-state energy for multi-dimensional polarons in symmetric quantum dots for arbitrary electron-phonon coupling constants are derived. Moreover, in the weak-coupling limit, the previous results by the second-order Rayleigh-Schrodinger perturbative theory are completely recovered. More interestingly, the extended- and localized-state solutions to the ground-state energy are obtained analytically.