Abstract: By discuss parameter representation, ing the relationship between the coordinate representation and the discretional mechanical this paper analyses the origin of the δ function normalization of eigenfunction with continuous eigenvalue. A conclusion is obtained that the eigenfunction of coordinate in the discretional mechanical parameter representation and the eigenfunction of discretional mechanical parameter in the coordinate representation are conjugated complex number of each other. Using this conclusion we give a new physical explanation of the eigenfunction closure.

Key words: representation, eigenfunction, δ function normalization, closure, Fourier transition