  Merrifield's Variational Ansatz is extended so as to cover the case of two
electronic bands mixed by an Einstein phonon. The Hamiltonian is composed of
the local and kinetic (hopping) energies in the absence of vibrations, the
vibrational energy, and a mixing band-off-diagonal part linear in the
electron-phonon coupling, all expressed in second quantization terms. The
variational eigenstate is a linear combination of Merrifield states for either
electronic band. We derive equations for the phonon Fourier amplitudes and for
the fractional contribution of either electronic band.
