Motion of the Piezoelectric Polaron at Zero Temperature

We analyze a series of theories which are used to obtain the energy-momentum relation for the piezoelectric polaron. Perturbation theory cannot be trusted, because there is a degeneracy in the unperturbed energy levels. The Tamm-Dancoff one-quantum cutoff in this case diagonalizes the degenerate states exactly, but has other shortcomings. The intermediate coupling theory gives what we believe is a reasonable energymomentum relation, which starts out quadratically and becomes approximately linear as the velocity approaches the speed of sound.