Variational Path-Integral Study on Bound Polarons in Parabolic Quantum Dots and Wires

The expression of the ground-state energy of the electron coupled simultaneously with a Coulomb potential and a longitudinal-optical phonon field in parabolic quantum dots and wires is derived within the framework of Feynman variational path integral theory.We obtain a general result with arbitrary electron-phonon coupling constant,Coulomb binding parameters,and confining potential strength,which could be used for further numerical calculation of polaron properties.Moreover,it is shown that all the previous path-integral formulae for free polarons,bound polarons,and polarons confined in parabolic quantum dots and wires can be recovered in the present formalism.