四阶精度差分法解定态薛定谔方程
收稿日期: 2021-02-07
修回日期: 2021-03-28
网络出版日期: 2021-09-24
基金资助
山东大学教改项目(B201814， 2020XWKC014);山东省教育厅教改重点项目(Z2018B110)
Solving time-independent Schrödinger equation by the fourth-order accurate difference method
Received date: 2021-02-07
Revised date: 2021-03-28
Online published: 2021-09-24
刘展源, 关成波, 吕英波, 张 鹏, 丛伟艳 . 四阶精度差分法解定态薛定谔方程[J]. 大学物理, 2021 , 40(9) : 58 . DOI: 10.16854 / j.cnki.1000-0712.210063
equation， the mostly used difference formula is the central difference formula， which is
accompanied with a truncation error on the second-or- der of step-size. In this paper， the
fourth-order accurate difference formulas of the derivatives are derived by the
five-point polynomial interpolation， and used to solve time - independent Schrödinger
equation in several common potential wells. The numerical results show that， the
fourth - order accurate difference formula has better
convergence and higher precision than the common central difference formula.
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