equivalent classes of square – integrable functions in the hilbert space

In this paper we have discussed that the members of the hilbert space are indeed not square-integrable functions themselves, but rather the members are equivalent classes of these functions. contemplating on these functions compels us to make a distinction between two operators. first, the ordinary derivative , is just the usual partial differentiation which acts on the scalar function; and should not be considered as an operator which can act on the vectors in the hilbert space. second, unbounded operator , which is usually mixed up with the former.