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A numerical procedure based on the time‐dependent Schrödinger equation for the modeling of multidimensional mesoscopic devices is presented. The primary features of this numerical method are a tight‐binding formulation of the quantum mechanical Hamiltonian, an alternating direction implicit generalization of the Crank–Nicholson method for solving the discretized multidimensional time‐dependent Schrödinger equation, and a numerical implementation of absorbing boundary conditions for propagating wavefunctions at the open boundaries of the simulated region. To show the capabilities of the absorbing boundary scheme, numerical results are presented for the diffusion of localized wavepackets out of open simulation regions. As an application to mesoscopic systems, results are presented for the switching in a T‐structure quantum modulated transistor with a continuous input wavefunction.