Energy–momentum relations in polaron problems with arbitrary coupling

A theory is derived suitable to obtain the energy‐momentum dependence for an arbitrarily coupling polaron. Using a variational principle general expressions are given which describe this dependence when an arbitrary shape of the electron surface of constant energy is considered and the polarization field is approximated by any number of fictitious particles. This method is able to yield the lowest band of electrons interacting with any mode of lattice vibrations. In particular, numerical results for the energy, depending on the total momentum, are obtained for isotropic optical and piezoelectric polarons in a wide range of a dimensionless coupling constant. Comparison of the results with known ones (only weak and strong‐coupling limits were investigated earlier) shows, that the energy values presented lie lower, though they represent themselves an upper bound for the exact polaron energymomentum relation.