### Abstract

Original language | English |
---|---|

Pages (from-to) | - |

Number of pages | 17 |

Journal | JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL |

Volume | 49 |

Publication status | Published - 2016 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

*JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL*,

*49*, -.

**Non-self-adjoint Hamiltonians with complex eigenvalues.** / Bagarello, Fabio; Bagarello.

Research output: Contribution to journal › Article

*JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL*, vol. 49, pp. -.

}

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 - antilinear operators; intertwining relations; PT-quantum mechanics; Mathematical Physics; Physics and Astronomy (all); Statistical and Nonlinear Physics; Modeling and Simulation; Statistics and Probability

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

SP - -

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

ER -