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In the simulation of high frequency nanoscale semiconductor devices in which electromagnetic (EM) fields and carrier transport are coupled, and optoelectronic devices in which strong interactions between EM fields and charged particles exist, both the Maxwell's equations and the time-dependent Schrödinger equation (TDSE) need to be solved to capture the interactions between EM and quantum mechanics (QM). One of the numerical simulation methods for solving these equations is the finite difference time domain (FDTD) method. In this review paper, the development of FDTD method applied in EM and QM simulation is discussed. Several widely used FDTD techniques, i.e., explicit, implicit, explicit staggered-time, and Chebyshev methods, for solving the TDSE are introduced and compared. The hybrid approaches based on FDTD method, which are used to solve the Poisson-TDSE and Maxwell-TDSE coupled equations for EM-QM simulation, are also discussed. Furthermore, the applications of these simulation methods for nanoscale semiconductor devices and optoelectronic devices are introduced. Finally, a conclusion is given.

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