Solvable simulation of a double-well problem in -symmetric quantum mechanics

Within the framework of -symmetric quantum mechanics of bound states (which works with parity-pseudo-Hermitian Hamiltonians H = H† and real spectra) we mimic some effects of the double-well structure of potentials by a pair of δ functions with mutually complex conjugate strengths. The model is solvable by the standard matching technique and exhibits several interesting features. We observe an amazingly robust absence of any -symmetry breaking. A quasi-degeneracy which occurs in the high-energy domain is interpreted as a manifestation of certain 'quantum beats'.