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An efficient treatment is developed for the Schrödinger equation with a class of local absorbing boundary conditions, which are obtained by high order Padé expansions. These boundary conditions are significant in the simulation of open quantum devices. Based on the finite difference approximation in the interior domain, we construct a spectral collocation layer on the cell near the artificial boundary, in which the wave function is approximated by the Chebyshev polynomials. The numerical examples are given by using this strategy with increasingly high order of accuracy up to the ninth order.

Spectral Collocation Technique for Absorbing Boundary Conditions with Increasingly High Order Approximation