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The silicon nanowire transistor (SNWT) is a promising device structure for future integrated circuits, and simulations will be important for understanding its device physics and assessing its ultimate performance limits. In this work, we present a three-dimensional (3D) quantum mechanical simulation approach to treat various SNWTs within the effective-mass approximation. We begin by assuming ballistic transport, which gives the upper performance limit of the devices. The use of a mode space approach (either coupled or uncoupled) produces high computational efficiency that makes our 3D quantum simulator practical for extensive device simulation and design. Scattering in SNWTs is then treated by a simple model that uses so-called Büttiker probes, which was previously used in metal-oxide-semiconductor field effect transistor simulations. Using this simple approach, the effects of scattering on both internal device characteristics and terminal currents can be examined, which enables our simulator to be used for the exploration of realistic performance limits of SNWTs.