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