Polarons in Anisotropic Energy Bands

The polaron weak-coupling approximation has been applied to the problem of an electron on a spheroidal energy surface interacting with longitudinal optical phonons. The binding energy and effective masses are calculated. For SrTi${\mathrm{O}}_3$, where the observed masses are ${m_l}^{*}{m}_0=6.0\mathrm{}$ and $\frac{{m_t}^{*}}{m_0}=1.5\mathrm{}$, the calculated bare masses are 4.7 and 0.96, respectively, and the binding energy is 0.26 eV. It is also shown how the polaron properties may be calculated when the band edge is of the degenerate type.