Semi-exact Solutions of Konwent Potential

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2019,（2）
• 页码范围: 231-236
• 页数: 6页
• 语种: 英文
• DOI: 10.1088/0253-6102/71/2/231

摘要

In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions.We find that the solutions are given by the confluent Heun function.The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1.The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V0 and a.The wave functions are shrunk towards the origin with the increasing ｜A|.In particular,the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases.We notice that the energy levels εi increase with the increasing potential parameter |A|| ≥ 1,but the variation of the energy levels becomes complicated for [A[∈ (0,1),which possesses a double well.It is seen that the energy levels ei increase with |A| for the parameter interval A ∈ (-1,0),while they decrease with |A｜ for the parameter interval A ∈ (0,1).