Poschl-Teller Ⅰ势势代数及同谱势研究  

Study of Potential Algebra of Poschl-Teller Ⅰ Potential and Its Isospectral Potential

作　　者：熊露霖 谭鑫 罗光[1] XIONG Lulin;TAN Xin;LUO Guang(School of Physicsand 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：《重庆师范大学学报（自然科学版）》2022年第6期110-117,共8页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金青年项目(No.11404046);重庆市科学技术局自然科学基金(No.cstc2012jjA50018);重庆师范大学国家基金预研项目(No.16XYY31)。

摘　　要：【目的】Poschl-TellerⅠ势是超对称量子力学中为数不多的满足薛定谔方程并能精确求解的双参数势中的一种。研究精确求解该势的途径,用势代数精确求解它在超对称性完整和破缺条件下的能级;同时构造Poschl-TellerⅠ势的同谱势从而增加可精确求解的势数目。【方法】1)基于超对称量子力学理论,研究了Poschl-TellerⅠ势的双参数势代数,应用待定系数法和迭代法得到了势代数描述的形状不变性,当超对称性破缺时,通过两步法调整参数的方式得到势代数形式的形状不变性;2)通过形状不变性构造出一个新的超势族,使它与原势具有相同的能级,并作出能级图像进行精确对比。【结果】1)根据势代数计算并得到了超对称性完整时的对应能谱;2)通过两步法调整参数得到势代数的形状不变性,计算并得到了该势在超对称破缺情况下的能谱;3)对比图像发现该势族与原势拥有相同能级。【结论】1)对比采用势代数方法得到的计算结果与用求解薛定谔方程的方法得到的计算结果,发现两者完全一致,由此得出双参数势代数法是求解P9schl-TellerⅠ势能级的另一个新途径;2)势代数法在超对称性破缺情况下仍适用精确求解对应的薛定谔方程;3) Poschl-TellerⅠ势的同谱势族可极大丰富可精确求解势的数目。[Purposes]The Poschl-Teller Ⅰ potential is one of the few two-parameter potentials in supersymmetric quantum mechanics that satisfies Schrodinger’s equations and can be accurately solved. In order to increase the way to accurately solve the potential, the potential algebra is used to accurately solve its energy level under the condition of supersymmetry integrity and defection. At the same time, the isospectral potential of the P9 schl-Teller is constructed to increase the number of precise solvable potentials. [Methods]1) Based on the theory of supersymmetric quantum mechanics, the two-parameter potential algebra of the P9 schl-Teller Ⅰ potential was studied, and the shape invariance of the potential algebra description is obtained by applying the pending coefficient method and the iterative method. When the supersymmetry is broken, the shape invariance of the potential algebra form is obtained by adjusting the parameters in two steps. 2) Construct a new super-potential family through shape invariance, so that it has the same energy level as the original potential, and make an image of the energy level for accurate comparison. [Findings]1) The corresponding energy spectrum when the supersymmetry is calculated and obtained according to the potential algebra. 2) The shape invariance of the potential algebra is obtained by adjusting the parameters in two steps, and the energy spectrum of the potential under the condition of supersymmetric breaking is calculated and obtained. 3) Comparing the images, it is found that the potential family has the same energy level as the original potential. [Conclusions]1) Comparing the calculation results obtained by the potential algebra method with the calculation results obtained by solving the Schrodinger equation, it is found that the two are exactly the same, and it is concluded that the two-parameter potential algebra method is another new way to solve the potential energy level of P9 schl-TellerI. 2) The potential algebra method is still applicable in the case of solvi

关 键 词：超对称量子力学 可解势 同谱势 Poschl-TellerⅠ势 

分 类 号：O413.1[理学—理论物理]