Exact solutions of the Schrodinger equation for a class of hyperbolic potential well  

作　　者：Xiao-Hua Wang Chang-Yuan Chen Yuan You Fa-Lin Lu Dong-Sheng Sun Shi-Hai Dong 王晓华;陈昌远;尤源;陆法林;孙东升;董世海(School of Physics and Electronic Engineering,Yancheng Teachers University,Yancheng 224007,China;Research Center for Quantum Physics,Huzhou University,Huzhou 313000,China;Laboratorio de Information Cuantica,CIDETEC,Instituto Polit´ecnico Nacional,UPALM,C.P 07700,CDMX,Mexico)

机构地区：[1]School of Physics and Electronic Engineering,Yancheng Teachers University,Yancheng 224007,China [2]Research Center for Quantum Physics,Huzhou University,Huzhou 313000,China [3]Laboratorio de Informaci´on Cu´antica,CIDETEC,Instituto Polit´ecnico Nacional,UPALM,C.P 07700,CDMX,Mexico

出　　处：《Chinese Physics B》2022年第4期109-115,共7页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant No.11975196);partially by SIP,Instituto Politecnico Nacional(IPN),Mexico(Grant No.20210414)。

摘　　要：We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation into a confluent Heun differential equation and then construct a Wronskian determinant by finding two linearly dependent solutions for the same eigenstate.And then in terms of the energy spectrum equation which is obtained from the Wronskian determinant,we are able to graphically decide the quantum number with respect to each eigenstate and the total number of bound states for a given potential well.Such a procedure allows us to calculate the eigenvalues for different quantum states via Maple and then substitute them into the wave function to obtain the expected analytical eigenfunction expressed by the confluent Heun function.The linearly dependent relation between two eigenfunctions is also studied.

关 键 词：hyperbolic potential well Schrodinger equation Wronskian determinant confluent Heun function 

分 类 号：O175.29[理学—数学]