An alternating-direction hybrid implicit-explicit finite-difference time-domain method for the Schrödinger equation

This paper proposes a novel hybrid FDTD method for solving the time-dependent Schrödinger equation, which is fundamental modeling materials and designing nanoscale devices. The wave function propagated on nonuniform grids by applying explicit updates in part of grid implicit elsewhere. latter are based Alternating-Direction Implicit (ADI) scheme while former constructed with central difference time derivative. A rigorous stability analysis proves that spatial steps can be selectively removed from criterion thus combining unconditional ADI fast calculations. excels its flexibility efficiently discretizing balancing updates, as such expediting computations. Moreover, it retains linear complexity schemes respect to space time, making especially scalable numerically large problems. Several numerical experiments, including laterally tunnel-coupled quantum wire nanowire double-barrier resonant-tunneling diode, show validity demonstrating high accuracy decreased CPU compared traditional methods.