The energy spectrum of a polaron---an electron interacting with the longitudinal-optical phonons of a polar crystal---is studied with particular attention given to the region where the polaron excitation energy closely approaches the energy of a longitudinal-optical phonon. In this region, existing theories of the polaron spectrum are inadequate; in particular, the usual Rayleigh-Schr\"odinger perturbation theory is shown to be inconsistent. A self-consistent weak-coupling theory is developed, and a variational theory of the polaron spectrum which, for small coupling, reduces to this weak-coupling theory is presented. Whitfield and Puff, and Schultz have conjectured that the polaron energy $E\mathrm{E}p\mathrm{R}$ , bends over and becomes horizontal as the polaron momentum $p$ approaches from below the value at which the polaron excitation energy, $E(p)\ensuremath{-}E(0)$, becomes equal to the optical-phonon energy. Using the weak-coupling method of the present paper, this conjecture has been verified to lowest order and next higher order in the coupling constant.The energy spectrum of a polaron---an electron interacting with the longitudinal-optical phonons of a polar crystal---is studied with particular attention given to the region where the polaron excitation energy closely approaches the energy of a longitudinal-optical phonon. In this region, existing theories of the polaron spectrum are inadequate; in particular, the usual Rayleigh-Schr\"odinger perturbation theory is shown to be inconsistent. A self-consistent weak-coupling theory is developed, and a variational theory of the polaron spectrum which, for small coupling, reduces to this weak-coupling theory is presented. Whitfield and Puff, and Schultz have conjectured that the polaron energy $E\mathrm{E}p\mathrm{R}$, bends over and becomes horizontal as the polaron momentum $p$ approaches from below the value at which the polaron excitation energy, $E(p)\ensuremath{-}E(0)$, becomes equal to the optical-phonon energy. Using the weak-coupling method of the present paper, this conjecture has been verified to lowest order and next higher order in the coupling constant.

Physical ReviewApr 15, 196683 citations

Some questions in polaron theory

G. O. Balabanyan

Theoretical and Mathematical PhysicsFeb 1, 19820 citations

Aspects of Polaron Theory - Equilibrium and Nonequilibrium Problems

Nikolay N. Bogolubov, NICKOLAI N. BOGOLUBOV

Linear Polaron Model Equilibrium Thermodynamic State of Polaron System Kinetic Equations in Polaron Theory.

WORLD SCIENTIFIC eBooksJan 1, 20088 citations

On the Strong Coupling Techniques of Polaron Theory

J. T. Devreese, R. P. Evrakd

De Gruyter eBooksDec 31, 19650 citations

E\mathrm{E}p\mathrm{R}

, bends over and becomes horizontal as the polaron momentum

p

approaches from below the value at which the polaron excitation energy, $E(p)\ensuremath{-}E(0)$, becomes equal to the optical-phonon energy. Using the weak-coupling method of the present paper, this conjecture has been verified to lowest order and next higher order in the coupling constant.