The doublet representation of non-Hilbert eigenstates of the Hamiltonian
Mario Castagnino, Graciela Domenech, Marcelo Leonardo Levinas, Norberto Umerez · Journal of Mathematical Physics · 1996
We find the minimal mathematical structure to represent quantum eigenstates with complex eigenvalues with no need of analytic continuation. These eigenvectors build doublets in non-Hilbert spaces. We construct exact solutions for the Friedrichs model that continuously join the ones of the free Hamiltonian. We extend the Wigner operator to these non-Hilbert spaces and enlarge the concept of normalized vectors via the definition of the doublets. Making use of these doublets, we describe systems whose states have initial conditions out of Hilbert space.