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

作　　者：SARWAR Qanitah 黄振友 ZAHID Abdul Hannan XU Xin-Jian SARWAR Qanitah;HUANG Zhen-you;ZAHID Abdul Hannan;XU Xin-Jian(Department of Applied Mathematics,Nanjing University of Science and Technology,Nanjing 210094,China;Department of Chemical Engineering,University of Gujrat,Gujrat 50700,Pakistan;Key Laboratory for Soft Chemistry and Functional Materials,Ministry of Education,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[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

出　　处：《Chinese Quarterly Journal of Mathematics》2023年第1期50-61,共12页数学季刊（英文版）

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 

分 类 号：O187.1[理学—数学]