Non-standard and Numerov finite difference schemes for finite difference time domain method to solve one-dimensional Schrödinger equation

Lily Maysari Angraini (Program Studi Fisika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Mataram, NTB, Indonesia)
I Wayan Sudiarta (Program Studi Fisika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Mataram, NTB, Indonesia)

Journal of Physics: Theories and Applications
Vol 2, No 1 (2018): Journal of Physics: Theories and Applications

The purpose of  this paper is to show some improvements of the finite-difference time domain (FDTD) method using Numerov and non-standard finite difference (NSFD) schemes for solving the one-dimensional Schrödinger equation. Starting with results of the unmodified FDTD method, Numerov-FD and NSFD are applied iteratively to produce more accurate results for eigen energies and wavefunctios. Three potential wells, infinite square well, harmonic oscillator and Poschl-Teller, are used to compare results of FDTD calculations. Significant improvements in the results for the infinite square potential and the harmonic oscillator potential are found using Numerov-NSFD scheme, and for Poschl-Teller potential are found using Numerov scheme.