Vibrational frequency of strong-coupling impurity bound magnetopolaron in quantum rods

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. We study the vibrational frequency and the ground state binding energy of the strong-coupling impurity bound magnetopolaron in a quantum rod. The effects of the aspect ratio of the ellipsoid, the electron–phonon coupling strength, the cyclotron frequency of a magnetic field and the Coulomb bound potential are taken into consideration by using a 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 cyclotron frequency. The vibrational frequency and the ground state binding energy are an increasing functions of the electron–phonon coupling strength. The vibrational frequency and the ground state binding energy are increasing functions of the aspect ratio of the ellipsoid in the case of the aspect ratio of the ellipsoid greater than 1. However, they become decreasing ones for the aspect ratio of the ellipsoid smaller than 1. When the aspect ratio of the ellipsoid equal to 1, the vibrational frequency and the ground state binding energy have minimum values.