Energy levels of a polaron bound indirectly to impurity ions in a double qu
antum well system are calculated in the adiabatic approximation by means of
a perturbation method, in which the unperturbed system is treated by the v
ariational theory of Lee-Low-Pines. The polaron binding energy as well as i
mpurity energy levels are studied for variable well width, barrier thicknes
s and magnetic fields. It is shown that the electron-phonon interaction con
tributes greatly to the binding energy and must not be ignored in a system
of double quantum wells in any case.