time-dependent simulations of quantum waveguides using a time-splitting spectral method

the electron flow through quantum waveguides is modeled by the time-dependent schrödinger equation with absorbing boundary conditions, which are realized by a negative imaginary potential. the schrödinger equation is discretized by a time-splitting spectral method, and the quantum waveguides are fed by a mono-energetic incoming plane wave pulse. the resulting algorithm is extremely efficient due to the fast fourier transform implementation of the spectral scheme. numerical convergence rates for a one-dimensional scattering problem are calculated. the transmission rates of a two-dimensional t-stub quantum waveguide and a single-branch coupler are numerically computed. moreover, the transient behavior of a three-dimensional t-stub waveguide is simulated.