具有勢壘的Sturm-Liouville算子的特徵值和特徵函數

doi:10.13371/j.cnki.chin.q.j.m.2023.01.004

数学季刊 ›› 2023, Vol. 38 ›› Issue (1): 50-61.doi: 10.13371/j.cnki.chin.q.j.m.2023.01.004

具有勢壘的Sturm-Liouville算子的特徵值和特徵函數

1. Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing
210094, China; 2. Department of Chemical Engineering, University of Gujrat, Gujrat 50700, Pakistan;
3. Key Laboratory for Soft Chemistry and Functional Materials, Ministry of Education, Nanjing
University of Science and Technology, Nanjing 210094, China

收稿日期:2021-12-02 出版日期:2023-03-30 发布日期:2023-03-20
通讯作者: SARWAR Qanitah (1986-), female, native of Bahawalpur, Pakistan, engages in functional analysis and operator theory E-mail: qanitah.sarwar@hotmail.com
作者简介:SARWAR Qanitah (1986-), female, native of Bahawalpur, Pakistan, engages in functional analysis and operator theory; HUANG Zhen-you (1962-), male, native of Huainan, Anhui, professor of Nanjing University of Science and Technology, engages in functional analysis and operator theory; ZAHID Abdul Hannan (1986-), male, native of Bahawalpur, Pakistan, lecturer of University of Gujrat, engages in semiconductor synthesis and processing; XU Xin-Jian (1990-), male, native of Nanjing, Jiangsu, engages in functional analysis and operator theory.

On the Eigenvalues and Eigenfunctions of the Sturm-Liouville Operator with the Barrier Potential

1. Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing
210094, China; 2. Department of Chemical Engineering, University of Gujrat, Gujrat 50700, Pakistan;
3. Key Laboratory for Soft Chemistry and Functional Materials, Ministry of Education, Nanjing
University of Science and Technology, Nanjing 210094, China

Received:2021-12-02 Online:2023-03-30 Published:2023-03-20
Contact: SARWAR Qanitah (1986-), female, native of Bahawalpur, Pakistan, engages in functional analysis and operator theory E-mail: qanitah.sarwar@hotmail.com
About author:SARWAR Qanitah (1986-), female, native of Bahawalpur, Pakistan, engages in functional analysis and operator theory; HUANG Zhen-you (1962-), male, native of Huainan, Anhui, professor of Nanjing University of Science and Technology, engages in functional analysis and operator theory; ZAHID Abdul Hannan (1986-), male, native of Bahawalpur, Pakistan, lecturer of University of Gujrat, engages in semiconductor synthesis and processing; XU Xin-Jian (1990-), male, native of Nanjing, Jiangsu, engages in functional analysis and operator theory.

摘要/Abstract

摘要： We aim to find the eigenvalues and eigenfunctions of the barrier potential
case for Strum-Liouville operator on the finite interval [0 ,π ] when λ> 0. Generally, the
eigenvalue problem for the Sturm-Liouville operator is often solved by using integral
equations, which are sometimes complex to solve, and difficulties may arise in computing
the boundary values. Considering the said complexity, we have successfully developed
a technique to give the asymptotic formulae of the eigenvalue and the eigenfunction for
Sturm-Liouville operator with barrier potential. The results are of significant interest in
the field of quantum mechanics and atomic systems to observe discrete energy levels.

关键词: Sturm-Liouville operator, Eigenvalue, Eigenfunction, Barrier potential;
Asymptotic estimate

Abstract: We aim to find the eigenvalues and eigenfunctions of the barrier potential
case for Strum-Liouville operator on the finite interval [0 ,π ] when λ> 0. Generally, the
eigenvalue problem for the Sturm-Liouville operator is often solved by using integral
equations, which are sometimes complex to solve, and difficulties may arise in computing
the boundary values. Considering the said complexity, we have successfully developed
a technique to give the asymptotic formulae of the eigenvalue and the eigenfunction for
Sturm-Liouville operator with barrier potential. The results are of significant interest in
the field of quantum mechanics and atomic systems to observe discrete energy levels.

Key words: Sturm-Liouville operator, Eigenvalue, Eigenfunction, Barrier potential;
Asymptotic estimate

中图分类号:

O187.1

SARWAR Qanitah 黄振友 ZAHID Abdul Hannan. 具有勢壘的Sturm-Liouville算子的特徵值和特徵函數[J]. 数学季刊, 2023, 38(1): 50-61.

SARWAR Qanitah, HUANG Zhen-you, ZAHID Abdul Hannan, XU Xin-Jian. On the Eigenvalues and Eigenfunctions of the Sturm-Liouville Operator with the Barrier Potential[J]. Chinese Quarterly Journal of Mathematics, 2023, 38(1): 50-61.

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具有勢壘的Sturm-Liouville算子的特徵值和特徵函數

On the Eigenvalues and Eigenfunctions of the Sturm-Liouville Operator with the Barrier Potential

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