  We introduce the contracted plane waves (CPWs), which satisfy the periodic
gauge in the Brillouin-zone torus as in the case of usual Wannier functions.
CPWs are very simply given as the sum of plane waves. We will be able to use
CPWs instead of the Wannier functions for the interpolation of physical
quantities given as the function of wave vectors in BZ. Furthermore, it will be
easy to complement the set of Gaussian bases by CPWs.
