Abstract
Two alternative scenarios are shown possible in Quantum Mechanics working with non-Hermitian
PT−
symmetric form of observables. While, usually, people assume that
P
is a self-adjoint indefinite metric in Hilbert space (and that their
P−
pseudo-Hermitian Hamiltonians
H
possess the real spectra etc), we propose to relax the constraint
P=
P
†
as redundant. Non-Hermitian triplet of coupled square wells is chosen for illustration purposes. Its solutions are constructed and the observed degeneracy of their spectrum is attributed to the characteristic nontrivial symmetry
S=
P
−1
P
†
≠I
of the model
H
. Due to the solvability of the model the determination of the domain where the energies remain real is straightforward. A few remarks on the correct (albeit ambiguous) physical interpretation of the model are added.