Variational path-integral study on bound polarons in parabolic quantum dots and wires

The expression of the ground-state energy of an electron coupled simultaneo usly with a Coulomb potential and a longitudinal-optical phonon held in par abolic quantum dots and wires is derived within the framework of Feynman va riational path-integral theory. We obtain a general result with arbitrary e lectron-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 ah the previous path-inte gral formulae for free polarons, bound polarons, and polarons confined in p arabolic quantum dots and wires can be recovered in the present formalism.