The paper presents low-dimensional quantum models for atomistic transport in nanowire field-effect transistors. A variational method is developed to construct a small representative basis which reproduces physical states of a tight-binding Hamiltonian within an arbitrary energy window. The equivalent transport models with the basis-transformed Hamiltonian are constructed and tested for various silicon nanowire transistors. The small size of the model makes it a powerful tool to study atomistic quantum transport in the presence of inelastic scattering.