The Dirac Bra and Ket Formalism

The place of the Dirac formalism in quantum theory is investigated using rigged Hilbert spaces. Emphasis is laid on the representation of observables by continuous linear operators and on the existence of sufficient eigenkets. Using the concept of labeled observables, a canonical procedure is given for constructing a rigged Hilbert space and the bra and ket spaces are constructed for nonrelativistic quantum systems of n interacting particles. Spectral theory is investigated in this framework and the results are compared with the Dirac formalism.