基于Kratzer势的D维薛定谔方程的超对称求解  

Supersymmetric Solution of D-Dimensional Schr?dinger Equation Based on Kratzer Potential

作　　者：谭鑫 罗光[1] 熊露霖 TAN Xin;LUO Guang;XIONG Lulin(School 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：《重庆师范大学学报（自然科学版）》2021年第2期84-88,共5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】基于超对称量子力学方法,求解D维球对称修正Kratzer势和广义Kratzer势作用下的薛定谔方程。【方法】通过给出试探解的办法得到这两种势作用下的超势,确定了超对称伴随势,并得出对应的形状不变因子,进而解得两种势对应的D维球对称薛定谔方程。【结果】利用形状不变因子和升、降算符的作用分别得到了修正Kratzer势和广义Kratzer势作用下的D维球对称薛定谔方程的基态能量本征值与本征函数,进而得到激发态的能量本征值和本征函数。【结论】计算表明D维球对称条件下修正Kratzer势和广义Kratzer势作用下的薛定谔方程是可以通过超对称量子力学方法求解的,且当D=3时,可得三维修正Kratzer势和广义Kratzer势的能量本征值与本征波函数。[Purposes]Based on the supersymmetric quantum mechanics method,the D-dimensional Schr?dinger equation under the modified Kratzer potential and the generalized Kratzer potential is solved.[Methods]The partner potentials are given by the superpotential which obtained by giving trial solution.Further,from the partner potentials,additive constant is obtained.[Findings]The energy eigenvalue and eigenfunction of the ground state for the modified Kratzer potential and the generalized Kratzer potential are derived by using the additive constant and the lowing and raising operators,then the energy eigenvalues and eigenfunctions of the excited state are obtained respectively.[Conclusions]The calculations show that the D-dimensional Schr?dinger equation under the modified Kratzer potential and the generalized Kratzer potential can be solved by the supersymmetric quantum mechanics method.The energy eigenvalues and eigenfunctions of 3-dimensional modified Kratzer potential and generalized Kratzer potential will be explicit when D=3.

关 键 词：超对称量子力学 超势 广义Kratzer势 修正Kratzer势 

分 类 号：O413.1[理学—理论物理]