Abstract: 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.

Key words: δ function, bound state, energy level, wave function