TY - JOUR

T1 - Non-self-adjoint Hamiltonians with complex eigenvalues

AU - Bagarello, Fabio

AU - Bagarello, null

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Mathematical Physics

KW - Modeling and Simulation

KW - PT-quantum mechanics

KW - Physics and Astronomy (all)

KW - Statistical and Nonlinear Physics

KW - Statistics and Probability

KW - antilinear operators

KW - intertwining relations

KW - Mathematical Physics

KW - Modeling and Simulation

KW - PT-quantum mechanics

KW - Physics and Astronomy (all)

KW - Statistical and Nonlinear Physics

KW - Statistics and Probability

KW - antilinear operators

KW - intertwining relations

UR - http://hdl.handle.net/10447/194969

UR - http://iopscience.iop.org/article/10.1088/1751-8113/49/21/215304/pdf

M3 - Article

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

ER -