Abstract: It is pointed out that the assertion that the eigenfunction of the creation operator a⁺ is identically zero is not rigorous.On the contrary, the eigenfunction of a⁺ may be discussed by using the contour integral representation of δ function, the property of which and the relation with the eigenstate of the annihilation operator are discussed. Its applications, especially the application in thoroughly studying the inverse operator's properties, are presented. It is shown that the phase operator can also be represented by the inverse operator.