作为极限情况的δ函数势阱束缚态问题  

The problem ofδfunction potential bound state as the limit case of two solvable potentials

作　　者：张印杰[1] 阎玉立[1] ZHANG Yin-jie;YAN Yu-li(College of Physics Science and Technology,Hebei University,Baoding,Hebei 071002,China)

机构地区：[1]河北大学物理科学与技术学院,河北保定0710022

出　　处：《大学物理》2025年第2期41-44,共4页College Physics

基　　金：河北大学第十批教育教学改革研究项目(2023XJJG068)资助。

摘　　要：根据δ函数广义函数的特征,给出了δ函数的一些极限表达式.从这些表达式中选取了可与δ函数势阱对应的方形势阱和双曲正割的平方函数势阱,这两个势阱取极限后趋于δ函数势阱.这两个势阱中的束缚态问题可严格求解.对这些严格解取极限后,其束缚态能级和波函数与δ函数势阱的结果一致.According to the characteristic ofδfunction,it can be treated as the limits of some distribution functions.A few of such functions are given.From these functions,δfunction potential can be treated as the limit of square-well potential and the square of sech function potential.The bound state problem of these potential can be solved exactly.The bound state energy and eigenfunction ofδfunction potential are exactly the limit of corresponding results of these potentials.

关 键 词：Δ函数 束缚态 能级 波函数 

分 类 号：O413.1[理学—理论物理]