Swanson Hamiltonian: non-PT-symmetry phase

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