A new method using Fock space wave functions is proposed for studying resonant tunneling in semiconductor quantum wells. The use of binary occupation numbers as dynamical variables, rather than properties of individual electrons, manifestly takes account of electron statistics, which enables investigation of the influence of the Pauli principle on resonant tunneling in the presence of inelastic scattering. Applied to the evaluation of the resonant current in semiconductor heterostructures, our approach predicts considerable deviations from the one-electron and rate equations pictures.