Abstract: The Hamiltonian of the quantum rod (QR) with an ellipsoidal boundary is given after a coordinate trans-formation. Using the linear-combination operator and unitary transformation methods, the vibrational frequency and the ground-state energy of weak-coupling polarons are obtained. Numerical results illustrate that the vibrational frequency increases with the decrease of the effective radius R0 of the ellipsoidal parabolic potential and the aspect ratio e′ of the ellipsoid, and that the ground-state energy increases with the decrease of the effective radius R0 and the electron-LO-phonon coupling strength α. In addition, the ground-state energy decreases with increasing aspect ratio e′within 0 < e′ < 1 and reaches a minimum when e′ = 1, and then increases with increasing e′ for e′> 1.

Key words: quantum rod,  weak-coupling,  linear-combination operator,  polaron