一种构建非多项式QES势的方法  

A method for constructing non-polynomial QES potential

作　　者：胡富望 肖倍 HU Fu-wang;XIAO Bei(College of Physics and Electronic Engineering,Hainan Normal University,Haikou,Hainan 571158,China)

机构地区：[1]海南师范大学物理与电子工程学院,海南海口2571158

出　　处：《大学物理》2024年第4期10-14,共5页College Physics

摘　　要：构建准精确可解问题的方法有很多,例如超对称方法、Darboux方法、李代数方法等,但是这些方法构建的准精确可解问题往往得到的是多项式型的波函数.我们从一类含参变化的双势阱出发,研究了和参数相关的性质,并且发现了一种构建QES势的方法,这种方法构建的QES势有李代数结构,但波函数的形式是非多项式.There are many approachs to construct quasi-exact solvable problems,such as supersymmetric method,Darboux method,Lie algebra method,etc.,but the quasi-exact solvable problems constructed by these methods are often polynomial wave functions.Starting from a class of double well with parametric variation,we study the properties related to the parameters,and find a method to construct QES potential.The QES potential constructed by this method has Lie algebraic structure,but the form of the wave function is non-polynomial.

关 键 词：薛定谔方程 Huen函数 准精确可解 

分 类 号：O4-11.1[理学—物理]