Note on the unified Dirac--von Neumann formulation of quantum mechanics

It is demonstrated that the mathematical model of a rigged Hilbert space is ideally suited for obtaining a unified Dirac−von Neumann formulation of quantum mechanics. It is shown that the eigenbras of an observable A can be interpreted as weak derivatives of certain functionals associated with the resolution of identity Eu, u - (−∞, ∞), associated with A.