On the basis of the generalized Schr?dinger equation， a novel state-vector function that obeys photon motion equation under three quantum conditions has been constructed for a photon in one dimension, which can describe completely the properties of a photon as a relativistic free particle, including its energy and momentum and spin angular momentum. The state-vector function not only defines microscopic parameters such as the probability amplitude and the phase for a photon, but also relates them with the macroscopic polarization of a light beam. As an example, it successfully explains the puzzling polarization problem of a light beam.