The electronic normal modes of a finite translational polymer helix are found to be well approximated by sinusoidal standing waves of electronic polarization with either even or odd symmetry with respect to inversion through the chain center. The dipole and rotational strengths of the normal modes are expressed as products of two types of sums over the wave: (i) lattice sums which are independent of the structure within the unit cell and (ii) cell sums which contain the structural information of the unit cell. Owing primarily to the behavior of the lattice sums at low wavenumber k of the polarization wave, the dipole and rotational strengths of a single low-k mode tend to dominate the absorption and circular dichroic spectra. The dispersion relation between frequency and wavenumber is derived for the polarization waves, giving further relations for the phase velocity and group velocity of a traveling polarization wave. The results are illustrated by calculations for fully extended poly[(R)-beta-aminobutyric acid] chains.