INFLUENCE OF THE PARABOLIC POTENTIAL ON THE INTERACTION OF ELECTRON-CONFINED PHONONS IN A QUANTUM-WIRE

The Lee, Low and Pines' variational method is employed to study the in teraction of electron-confined phonons within a rectangular quantum wi re under an additional parabolic potential. Detailed mathematical deri vation is carried out to obtain some formulae for the polaron self-ene rgy, the electron effective mass along the wire and the ground state e nergy. Using the idea of Fourier decomposition of wavefunctions, numer ical calculations are performed for a typical GaAs quantum wire within the mesoscopic size. Our present results show that the effect of phon on confinement always reduces the magnitude of the electron-phonon int eraction and the associated physical quantities whereas the additional parabolic potential tends to enhance both the electron-phonon interac tion and the ground state energy. Comparing with previous calculations , our results also reveal the trends of those interesting physical qua ntities.