• Non-standard finite-difference time-domain method for solving the Schrödinger equation

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      https://www.ias.ac.in/article/fulltext/pram/091/04/0052

    • Keywords

       

      Time-dependent Schrödinger equations; non-standard finite difference method; finite-difference timedomain method; eigenvalues; eigenfunctions

    • Abstract

       

      In this paper, an improvement of the finite-difference time-domain (FDTD) method using a non-standard finite-difference scheme for solving the Schrödinger equation is presented. The standard numerical scheme for a second derivative in the spatial domain is replaced by a non-standard numerical scheme. In order to apply the non-standard FDTD (NSFDTD), first, the estimates of eigenenergies of a system are needed and computed bythe standard FDTD method. These first eigenenergies are then used by the NSFDTD method to obtain improvedeigenenergies. The NSFDTD method can be employed iteratively using the resulting eigenenergies to obtain moreaccurate results. In this paper, the NSFDTD method is validated using infinite square well, harmonic oscillator andMorse potentials. Significant improvements are found when using the NSFDTD method.

    • Author Affiliations

       

      I WAYAN SUDIARTA1

      1. Physics Study Program, Faculty of Mathematics and Natural Sciences, University of Mataram, Mataram, NTB, Indonesia
    • Dates

       
  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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