The Ground State of the Optical Polaron in the Strong-Coupling Case

The next lowest order term of the ground state energy has its origin in lowering of frequencies of phonons localized around the polaron. An eigenvalue equation is derived, the solution of which gives phonon eigenmodes and frequencies in the presence of the polaron. Several eigenvalues are obtained by numerical integration. From the results, the ground state energy is estimated as \(E₀/ω₀{=}-0.108513α²-2.836+O(1/α²)\), where ω 0 is the frequency of the optical phonon and α is the electron-phonon coupling constant. The numerical value of the effective mass is 0.0227019α 4 .