image-site-lattice analogues of image Original Research Article

A discrete image-level alternative to the popular imaginary cubic oscillator is proposed and studied. As usual, the unitarity of evolution is guaranteed by the introduction of an ad hoc, Hamiltonian-dependent inner-product metric, the use of which defines the physical Hilbert space and renders the Hamiltonian (with real spectrum) observable. Due to the simplicity of our model of dynamics the construction of the set of eligible metrics is shown tractable by non-numerical means which combine the computer-assisted algebra with the extrapolation and/or perturbation techniques.