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 of δ function, it can be treated as the limits of some distribution functions. A few of such functions are given. From these functions, δ function 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 of δ function potential are exactly the limit of corresponding results of these potentials.