Scattering in PTPT-symmetric quantum mechanics

A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of PP, TT or PTPT invariance of the Hamiltonian. Applications to some solvable PTPT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PTPT symmetry and the peculiarities of separable kernels of non-local potentials in connection with Hermiticity, TT invariance and PTPT invariance.