Swanson Hamiltonian: non-PT-symmetry phase

Abstract

In this work, we study the non-Hermitian Swanson Hamiltonian, particularly the non-parity-time 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.