Abstract
The Hamiltonian of a quantum rod (QR) with an ellipsoidal boundary is given after a coordinate transformation, which changes the ellipsoidal boundary into a spherical one. We then study the eigenenergies and eigenfunctions of the ground and the first excited states of an electron strongly coupled to the LO-phonon in the QR under a magnetic field. The present system may be used as a two-level qubit. When the electron is in the superposition state of the ground and the first excited states, we obtained the time evolution of the electron probability density oscillating in the QR. It is found that the magnitude of the probability density is increased by the magnetic field, whereas it decreases the oscillation period of the probability density. The oscillation period is a increasing function of the ellipsoid aspect ratio, the transverse and longitudinal effective confinement lengths of the QR, but a decreasing one of the electron-phonon coupling strength and the cyclotron frequency of the magnetic field.
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