Continuum states in generalized Swanson models

Abstract

A one-to-one correspondence is known to exist between the spectra of the discrete states of the non Hermitian Swanson-type Hamiltonian $ H = {\cal{A}}^{\dagger} {\cal{A}} + α{\cal{A}} ^2 + β{\cal{A}}^{\dagger 2} $, ($α\neq β$), and an equivalent Hermitian Schrödinger Hamiltonian $h$, the two Hamiltonians being related through a similarity transformation. In this work we consider the continuum states of $h$, and examine the nature of the corresponding states of $H$.

12 pages, 2 figures