Impurity Effect of a Bound Polaron in Quantum Rods

Based on a coordinate transformation, we first change the boundary potential of a quantum rod from the ellipsoidal form into a spherical one. And then the properties of the vibrational frequency and the ground state binding energy of a strongly-coupled impurity bound polaron in it are studied. The effects of the ellipsoid aspect ratio, the electron-phonon coupling strength, the Coulomb bound potential and the transverse and longitudinal effective confinement lengths are taken into consideration by using the linear combination operator method. It is found that the vibrational frequency and the ground state binding energy will increase with increasing Coulomb bound potential and the electron-phonon coupling strength. They are decreasing functions of the ellipsoid aspect ratio and the transverse and longitudinal effective confinement lengths.