Precise numerical solutions of potential problems using the Crank-Nicolson method

Daekyoung Kang, E. Won

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We present a numerically precise treatment of the Crank-Nicolson method with an imaginary time evolution operator in order to solve the Schrödinger equation. The time evolution technique is applied to the inverse-iteration method that provides a systematic way to calculate not only eigenvalues of the ground-state but also of the excited-states. This method systematically produces eigenvalues with the accuracy of eleven digits when the Cornell potential is used. An absolute error estimation technique is implemented based on a power counting rule. This method is examined on exactly solvable problems and produces the numerical accuracy down to 10- 11.

Original languageEnglish
Pages (from-to)2970-2976
Number of pages7
JournalJournal of Computational Physics
Volume227
Issue number5
DOIs
Publication statusPublished - 2008 Feb 20

Keywords

  • Crank-Nicolson method
  • Finite differences
  • Imaginary time
  • Precise numerical calculation
  • Schrödinger equation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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