Perturbation Theory for a Bound Polaron

The binding energy of a polaron in a Coulomb potential is determined by the second-order perturbation theory to be $E_B^{\mathrm{}\left(2\right)\mathrm{}}=E_B+\alpha \hslash {\omega }_0(\frac{1}{6}{\beta }^2+\frac{1}{24}{\beta }^4)$, where $\alpha$ is the Fröhlich coupling constant and ${\beta }^2=\frac{E_B}{\hslash {\omega }_0}$. It is supposed that $\alpha \ll 1$ and $\beta \ll 1$. This improves the earlier calculation of Platzman and brings the perturbation theory to agreement with the result reached previously by the application of field-theoretic methods to the problem of a bound polaron.