Abstract
The concept of point interactions offers one of the most suitable guides towards a quantitative analysis of properties of certain specific non-Hermitian (so-called -symmetric) quantum-mechanical systems. This is illustrated with a double-well model, the easy solvability of which is shown to lead to a clear picture of the mechanisms of the unavoided level crossing and of the spontaneous -symmetry breaking at a certain strong-non-Hermiticity boundary. Below this limit the model is shown to be suitable for an explicit illustration of technicalities related to the standard probabilistic physical interpretation of bound states in -symmetric quantum mechanics.
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