Calculation of longitudinal optical (LO) mode potential functions and dispersion curves are made for a AlAs/GaAs/AlAs quantum well using a macroscopic model. The interface boundary conditions employed are continuity of potential and normal components of both electric flux density and relative ionic displacement. In the non-dispersive limit the model yields unique potential functions of two types: confined modes and interface modes. The confined mode potential functions are almost identical to those calculated for a microscopic model by Huang and Zhu (1988). The interface modes are identical to these predicted by both the microscopic model and the dielectric continuum model. The introduction of bulk dispersion in GaAs produces modes which are hybrids of the confined and interface phonons.