A generalization of the three-dimensional Fröhlich hamiltonian for a polar semiconductor is presented which describes the interaction between charge carriers of a zero-dimensional electron gas and longitudinal optical (LO) phonon modes confined in three spatial dimensions. This hamiltonian is used to calculate the scattering rate of electrons by LO phonons in a GaAs quantum box which is free-standing in vacuum. The suppression of scattering through a phonon bottleneck effect is discussed in terms of the selection rules. © 1993 Academic Press. All rights reserved.