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The Hamiltonian of the quantum rod (QR) with an ellipsoidal boundary is given after a coordinate transformation. 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.
The Hamiltonian of the quantum rod (QR) with an ellipsoidal boundary is given after a coordinate transformation. The linear-combination operator and unitary transformation methods, the vibrational frequency and the ground-state energy of weak-coupling polarons are obtained. 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 of 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 1.