  In this work, we study the non-hermitian Swanson hamiltonian, particularly
the non-PT symmetry phase. We use the formalism of Gel'fand triplet to
construct the generalized eigenfunctions and the corresponding spectrum.
Depending on the region of the parameter model space, we show that the Swanson
hamiltonian represents different physical systems, i.e. parabolic barrier,
negative mass oscillators. We also discussed the presence of Exceptional Points
of infinite order.
