  The properties of the polaron and bipolaron are explored in the 1D
Jahn-Teller model with dynamical quantum phonons. The ground-state properties
of the polaron and bipolaron are computed using a recently developed
variational method. Dynamical properties of the ground state of a polaron are
investigated by calculating the optical conductivity $\sigma(\omega)$. Our
numerical results suggest that the Jahn-Teller and Holstein polarons are
similar. However, in the strong-coupling regime qualitative differences in
$\sigma(\omega)$ between the two models are found and discussed. The influence
of the electron-phonon coupling and the electrostatic repulsion on the
bipolaron binding energy, bipolaron masses, and correlation functions is
investigated.
