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Quantum-mechanical modeling of ballistic transport in nanodevices usually requires solving the Schrödinger equation at multiple energy points within an energy band. To speed up the simulation and analysis, the asymptotic waveform evaluation is introduced in this paper. Using this method, the wave function is only rigorously solved at several sampled energy points, whereas those at other energies are computed through Padé approximation. This allows us to obtain the physical quantities over the whole energy band with very little computational cost. In addition, the accuracy is controllable by a complex frequency hopping algorithm. The validity and efficiency of the proposed method are demonstrated by detailed study of several multigate silicon nano-MOSFETs.