Properties of Weak-coupling Impurity Bound Polaron in a Quantum Rod

The Hamiltonian of a quantum rod with an ellipsoidal boundary is given after a coordinate transformation which can transform the boundary into a spherical one.The relations of the vibrational frequency,the ground state energy and the ground state binding energy of weak-coupling impurity bound polaron in a quantum rod with the Coulomb bound potential,the electron-phonon coupling strength and the aspect ratio of the ellipsoid are studied by using the linear combination operator and the unitary transformation methods.Numerical calculations are performed and the results show that they will increase with increasing Coulomb bound potential.The ground state energy and the ground state binding energy are increasing functions of the electron-phonon coupling strength.The vibrational frequency,the ground state energy and the ground state binding energy are increasing functions of the aspect ratio of the ellipsoid when e'1,whereas they are decreasing functions of one when e'1.When e'=1,the vibrational frequency is a minimum value and the ground state energy and the ground state binding energy are a less steady value.