Spatial confinement, non-Hermitian Hamiltonians and related problems

We treat simple examples of systems described by non-relativistic model Hamiltonians which are unconventional. They are not necessarily Hermitian operators. In practice, they often contain applied external fields which are not necessarily small, and they seek to describe the effects of spatial confinement more realistically than most of the classic calculations (some of them by the present authors). A much studied model of a free particle confined by a non-real potential can be accommodated within the same theoretical framework. Numerical treatment of these and similar problems seems well within the capacity of very modest computer systems, as exemplified by a few tabulations.