Abstract: The Hamiltonian of a quantum rod with an ellipsoidal boundary is given after a coordinate transformation which changes the ellipsoidal boundary into a spherical one. We then study the first internal excited state energy, the excitation energy and the frequency of the transition spectral line between the first internal excited state and the ground state of the strong-coupling polaron in a quantum rod. The effects of the electron–phonon coupling strength, the aspect ratio of the ellipsoid, the transverse radius of quantum rods and the transverse and longitudinal effective confinement length are taken into consideration by using a linear combination operator and the unitary transformation methods. It is found that the first internal excited state energy, the excitation energy and the frequency of the transition spectral line are increasing functions of the electron–phonon coupling strength, whereas they are decreasing ones of the transverse radius of quantum rods and the aspect ratio. The first internal excited state energy, the excitation energy and the frequency of the transition spectral line increase with decreasing transverse and longitudinal effective confinement length. oindent

Key words: quantum rods, polaron, linear combination operator, aspect ratio