Nonstandard Finite Difference Time Domain (NSFDTD) Method for Solving the Schrödinger Equation
arXiv:1706.01999 · doi:10.1007/s12043-018-1632-z
Abstract
In this paper, an improvement of the finite difference time domain (FDTD) method using a non-standard finite difference scheme is presented. The standard numerical scheme for the second derivative in the spatial domain is replaced by a non-standard numerical scheme. In order to apply the non-standard FDTD (NSFDTD), first estimates of eigen-energies of a system are needed and computed by the standard FDTD method. These first eigen-energies are then used by the NSFDTD method to obtain improved eigen-energies. The NSFDTD method can be performed iteratively using the resulting eigen-energies to obtain accurate results. In this paper, the NS-FDTD method is validated for infinite square well, harmonic oscillator and Morse potentials.
8 pages, 3 figures
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