In recent years

the development of molecular-beam epitaxy techniques and metal-organic chemical-vapor deposition techniques have made possible the fabrication of quantum well structures in which the electrons are confined to move in one or two dimensions. Due to their small sizes these structures present some special physical properties. Optical and electronic properties of quantum wells

quantum wires and quantum dots have been the subject of both theoretical and experimental investigations in recent years. Polaron in quantum wires are markedly different from those in bulk materials

due to the presence of wire potentials with the form V

which confine the carriers motion in the ρ-plane transverse to the wire axis. The confining potential may bring out many rich phonon modes such as confined phonon modes

interface phonon modes

etc

. Even for the confined phonon itself

there are so many types: rectangular

cylindrical and parabolic types. A variety of phonon modes and various types of the wire potential have given rise to rich and varied investigations in this field. For the energies of polaron problems in QW

few author studied energies of polaron itself. In this paper

by solving the effective mass equation with the variational method

we have studied the ground state energies and the electron-phonon interaction energies of polaron in cylindrical quantum wires.The energies of the ground state and the absolute value of the electron-LO phonon interaction energies were given. The numerical results show

with the decreasing radius of the quantum wires

the ground state energies and the absolute value of the electron-LO phonon interaction energies increase mononically.