Numerical Methods for the Eigenvalue Determination of Second-Order Ordinary Differential Equations and Their Applications to Quantum Mechanics

DOI Web Site Web Site 1 Citations 107 References

Bibliographic Information

Other Title
  • 二階線型常微分方程式の固有値問題の高精度数値解法と量子力学への応用
  • ニカイ センケイ ジョウビブン ホウテイシキ ノ コユウチ モンダイ ノ コウセイド スウチ カイホウ ト リョウシ リキガク エノ オウヨウ

Search this article

Abstract

Numerical methods for the eigenvalue problem of second-order ordinary differential equations are presented. One is the discretized matrix eigenvalue method and another is the shooting method. In the former method, derivative with respect to spatial coordinate is discretized, thus the ordinary differential equation is transformed into matrix eigenvalue problems, then the matrix eigenvalue problems are solved numerically. The latter method has three steps. Firstly, initial values for the eigenvalue and eigenfunction at both ends are obtained by using the discretized matrix eigenvalue method. Secondly, the initial-value problem is solved using new, highly accurate formulas of the linear multistep method. Thirdly, the eigenvalue is properly corrected at the matching point. The efficiency of the proposed methods is demonstrated by their applications to bound states for the one-dimensional harmonic oscillator and anharmonic oscillators, the Morse potential and the modified Pöschl-Teller potential in quantum mechanics.

Journal

Citations (1)*help

See more

References(107)*help

See more

Keywords

Details 詳細情報について

Report a problem

Back to top