Non-self-adjoint Hamiltonians with complex eigenvalues
- Authors: Bagarello, F.
- Publication year: 2016
- Type: Articolo in rivista (Articolo in rivista)
- Key words: antilinear operators; intertwining relations; PT-quantum mechanics; Mathematical Physics; Physics and Astronomy (all); Statistical and Nonlinear Physics; Modeling and Simulation; Statistics and Probability
- OA Link: http://hdl.handle.net/10447/194969
Abstract
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.