This paper has given the analytical representations the potential matrix elements when solving Schrodinger equation diedy in nonregular hyperspherical coordinates , and also given the induced proass.

By the method of linear transformation, the solution forms of vector wave equation in spherical coordinates, l, m and n, are transformed to the many other kinds of forms.

In this paper, the symmetry of curved lined given by parametric equation and polar coordinates equation is discussed and the sufficient conditions are given.