The properties of polarons in zinc-blende and wurtzite GaN/AlN quantum wells with Fr(o|¨)hlich interaction Hamiltonians are compared in detail.The energy shifts of polarons at ground state due to the interface(IF), confined(CO) and half-space phonon modes are calculated by a finite-difference computation combined with a modified LLP variational method.It is found that the two Fr(o|¨)hlich interaction Hamiltonians are consistent with each other when the anisotropic effect from the z-direction and the x-y plane is neglected.The influence of the anisotropy on the polaron energy shifts due to the IF phonon modes for a smaller well width or due to the CO phonon modes for a moderate well width is obvious.In addition,the built-in electric field has a remarkable effect on the polaron energy shifts contributed by the various phonon modes. The properties of polarons in zinc-blende and wurtzite GaN / AlN quantum wells with Fr (o | ¨) hlich interaction Hamiltonians are compared in detail. The energy shifts of polarons at ground state due to the interface (IF), confined (CO) and half-space phonon modes are calculated by a finite-difference computation combined with a modified LLP variational method. It is found that the two Fr (o | ¨) hlich interaction Hamiltonians are consistent with each other when the anisotropic effect from the z- direction and the xy plane is neglected. The influence of the anisotropy on the polar energy shifts due to the IF phonon modes for a smaller well width or due to the CO phonon modes for a moderate well width is obvious. In addition, the built- in electric field has a remarkable effect on the polar energy shifts contributed by the various phonon modes.