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 $H={\mathcal{A}}^{†}\mathcal{A}+\alpha {\mathcal{A}}^2+\beta {\mathcal{A}}^{†2}$, ($\alpha \ne \beta$), 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