Bagarello, F. Non-self-adjoint Hamiltonians with complex eigenvalues. (English) Zbl 1344.81084 J. Phys. A, Math. Theor. 49, No. 21, Article ID 215304, 13 p. (2016). Summary: Motivated by what one observes dealing with PT-symmetric quantum mechanics, we discuss what happens if a physical system is driven by a diagonalizable Hamiltonian with not all real eigenvalues. In particular, we consider the functional structure related to systems living in finite-dimensional Hilbert spaces, and we show that certain intertwining relations can be deduced also in this case if we introduce suitable antilinear operators. We also analyze a simple model, computing the transition probabilities in the broken and in the unbroken regime. Cited in 5 Documents MSC: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 81R40 Symmetry breaking in quantum theory 81R12 Groups and algebras in quantum theory and relations with integrable systems Keywords:PT-quantum mechanics; antilinear operators; intertwining relations PDFBibTeX XMLCite \textit{F. Bagarello}, J. Phys. A, Math. Theor. 49, No. 21, Article ID 215304, 13 p. (2016; Zbl 1344.81084) Full Text: DOI arXiv