### Abstract

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

Pages (from-to) | 424-435 |

Number of pages | 12 |

Journal | Annals of Physics |

Volume | 362 |

Publication status | Published - 2015 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*362*, 424-435.

**Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces.** / Bagarello, Fabio; Bagarello.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 362, pp. 424-435.

}

TY - JOUR

T1 - Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

AU - Bagarello, Fabio

AU - Bagarello, null

PY - 2015

Y1 - 2015

N2 - In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we will find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.

AB - In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we will find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.

UR - http://hdl.handle.net/10447/147453

UR - http://www.elsevier.com/inca/publications/store/6/2/2/7/8/4/index.htt

M3 - Article

VL - 362

SP - 424

EP - 435

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -