We present a new method to calculate the dispersion relation of the light-excition coupled state propagating in a waveguide containing a single quantum well on the basis of the additional-boundary-condition-free polariton theory developed by Cho. The numerical computation of the dispersion relation for the TE-mode is carried out in the energy region near the heavy-hole exciton state of a GaAs/AlGaAs quantum well. The group velocity and the absorption rate obtained from the dispersion relation are in reasonable agreement with time-of-flight measurements.