A non-perturbative approach to the coupled electron optical phonon system

The usual approach to a localised electron coupled to the optical phonon field of a polar crystal is perturbative and therefore subject to restrictions on α(the Froehlich coupling constant) and β(the Platzman parameter). A new method, essentially an iterative variational one, is proposed here for unrestricted values of α and β. The hamiltonian of electron (hsub(e)), phonons (hsub(p)), and electron-phonon interaction (hsub(ep)) is reduced by successive variational treatment such that at each order the structure of the hamiltonian is maintained with re-defined hsub(e), hsub(p) and hsub(ep). The new hsub(p) describes a displaced phonon field and the shift in the bound polaron energy is now obtained directly from the solution of the new hsub(e) of a chosen order of iteration variation. The lowest order shift when calculated in this way yields the result Δ=-5/8.αβ which was suggested earlier by Harper (Antwerp Summer School, 1971) from a consideration of the optical absorption energy. This is also suprisingly close to the perturbation result of Mitra (1972) but is now free from any constraints on the parameters. (auth.)