Numerical analysis on Schrödinger equation using the finite difference method; [유한차분법을 이용한 슈뢰딩거 방정식의 수치해석]

초록

The finite difference method (FDM) is a numerical technique used for solving partial differential equations with boundary conditions, such as the Navier-Stokes equation, by uniformly dividing the domain. In this method, the granularity of the domain division determines both accuracy and computational workload, together with the number of grids being a critical parameter. Additionally, numerical errors arise when an unbounded domain is truncated to a finite one during numerical computations. This study aims to analyze relative errors for the 1D infinite well, the 1D harmonic oscillator, and the Coulomb potential, depending on the spacing grid and the range of the domain. Furthermore, energies for the Yukawa potential from 1s to 3d states are computed using the same conditions with the least error obtained from the Coulomb potential. These computed results are then compared with those from other methods to validate the reliability of our results. © 2025 Korean Physical Society. All rights reserved.

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