Compact Form Of Generalized Finite Difference Time Domain Method For Solving Schrodinger Equation

The Finite-Diference Time-Domain (FDTD) method is a well-known technique forthe analysis of quantum devices. It solves a discretized Schr¨odinger equation in an iterativeprocess. However, the method provides only a second-order accurate numerical solutionand requires that the spatial grid size and time step should satisfy a very restricted condi-tion in order to prevent the numerical solution from diverging. In this thesis, the compactforms of generalized FDTD method for solving the time-dependent Schr¨odinger equationare proposed. A more relaxed condition for stability is obtained, so that a larger timestep can be used in order to speed up the computation. This is particularly importantfor long period quantum computation. The obtained generalized FDTD compact schemesare tested by several numerical examples including the simulation of a particle movingin free space and then hitting an energy potential. Numerical results coincide with thoseobtained based on the theoretical analysis.