Mobility of the Lee-Low-Pines Polaron

The Low-Pines polaron mobility calculation is discussed. It is pointed out that the optical theorem provides an alternative method for evaluating the mobility from the Low-Pines scattering matrix. The application of this method leads to the mobility formula $\mu =\left(\frac{e}{2\alpha \overline{N}\omega m^{*}}\right)f\left(\alpha \right),$ where $f\left(\alpha \right)$ is the slowly varying function calculated by Low and Pines. A sample calculation is performed to illustrate why the above formula is to be preferred. The above modification of the original Low-Pines formula not only agrees with perturbation theory to order ${\alpha }^0$, but is also in fair agreement with Osaka's Feynman-model calculation for $\alpha \lesssim 3$.