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Journal of Inner Mongolia University for Nationalities

The Bound Optical Polaron in a Coulomb Potential

Xiao Jing-lin

Published Jan 1, 2003• 0 citations
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Abstract

In this paper,the properties of the bound optical polaron in Coulomb potential is studied,which is valid for the whole range of the electron-phonon coupling.The energy of the ground state and of the first excited state of the bound optical polaron is calculated for different values of the electro-phonon coupling using linear combination operator and unitary transformation methods.

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International Journal of Modern Physics B•Feb 15, 1996•0 citations
In this paper,the properties of the bound optical polaron in Coulomb potential is studied,which is valid for the whole range of the electron-phonon coupling.The energy of the ground state and of the first excited state of the bound optical polaron is calculated for different values of the electro-phonon coupling using linear combination operator and unitary transformation methods.
The optical polaron bounded in a Coulomb potential is investigated within the modified variational scheme of the Lee-Low-Pines theory (1953) which is valid for the whole range of the electron-phonon coupling. The ground state energy, the mean number of phonons in the cloud around the electron and the spatial localisation of the electron for the optical polaron change abruptly at certain values of the electron-phonon coupling constant alpha and of the Coulomb potential beta . The polaron changes its state according to the values of the parameters alpha and beta . Such features are summarised in the phase diagram.
Based on the unitary transformation, a general treatment of the bound polaron is proposed. In distinction from earlier calculations, the present method gives explicit expressions for not only the energy but also the wave functions both in the ground state and in the excited states such as the relaxed excited state and the phonon scattering state. These expressions involve a summation on the complete set of eigenstates of a trial Hamiltonian, and in actual calculations the Coulomb Hamiltonian and the harmonic oscillator Hamiltonian are chosen as trial Hamiltonians. For the ground state, the energy expression is the same as that obtained by Matsuura with the path integral method. The present method is valid in the whole region of the electron-phonon coupling constant α and Coulomb force β except for β→0 and α>6.