Strong-Coupling Limit of the Polaron Ground State

In the strong-coupling limit, the polaron ground state energy has been known to be proportional to α 2 , α being the electron-phonon coupling constant. The coefficient of proportionality is found by numerical calculation to be 0.108513 in an appropriate unit. Pekar's variational function is found to give an excellent approximate solution; the energy differs by less than 0.01%, and the error in wave function is less than 1% where the value of the wave function is appreciable.