基于SUSYQM的双曲Pöschl-Teller超势的形状不变性及势代数研究  

The shape invariance and Potential Algebra of the hyperbolic Pöschl-Teller potential based on SUSYQM

作　　者：程魏 罗光[1] 刘瑶 CHENG Wei;LUO Guang;LIU Yao(College of Physics and Electronic Engineering,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学物理与电子工程学院,重庆401331

出　　处：《大学物理》2024年第10期13-20,35,共9页College Physics

基　　金：重庆市科委自然科学基金(cstc2021jcyj-msxmX0168);重庆市教委研究生教育教学改革研究项目(yjg213067)资助。

摘　　要：双曲Pöschl-Teller势是超对称量子力学中已知可解势中少数含有两个参数的势,且该势参数在满足形状不变性的条件下呈现出一种交错加性.本文探究了双参数交错加性对对应能级与波函数带来了怎样的变化.本文用超对称量子力学方法和势代数法精确求解了双曲Pöschl-Teller势在双参数加性变化下对应的能量本征值和本征波函数.两种方法所求结果保持一致,相互对应,且参数的交错加性变化使得双曲Pöschl-Teller势对应的能级与波函数产生了部分缺失.The hyperbolic Pöschl-Teller potential is one of the few known solvable potentials in supersymmetric quantum mechanics that contains two parameters,and this potential's parameters exhibit a cross-additivity change under the condition of shape invariance.This article explores how the two parameters' cross-additivity affects the corresponding energy levels and wave functions.This paper uses supersymmetric quantum mechanics and potential algebra methods to accurately solve the energy eigenvalues and eigenwave functions corresponding to the hyperbolic Pöschl-Teller potential with the cross-additivity of two parameters.The results obtained by the two methods are consistent and correspond to each other.And the cross-additivity changes in parameters result in partial missing energy levels and wave functions of the hyperbolic Pöschl-Teller potential.

关 键 词：超对称量子力学 超势 双参数交错加性 形状不变性 

分 类 号：O413.1[理学—理论物理]