### Abstract

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

Pages (from-to) | 2526-2532 |

Number of pages | 7 |

Journal | PHYSICS LETTERS A |

Volume | 382 |

Publication status | Published - 2018 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*PHYSICS LETTERS A*,

*382*, 2526-2532.

**Finite-dimensional pseudo-bosons: A non-Hermitian version of the truncated harmonic oscillator.** / Bagarello, Fabio; Bagarello.

Research output: Contribution to journal › Article

*PHYSICS LETTERS A*, vol. 382, pp. 2526-2532.

}

TY - JOUR

T1 - Finite-dimensional pseudo-bosons: A non-Hermitian version of the truncated harmonic oscillator

AU - Bagarello, Fabio

AU - Bagarello, null

PY - 2018

Y1 - 2018

N2 - We propose a deformed version of the commutation rule introduced in 1967 by Buchdahl to describe a particular model of the truncated harmonic oscillator. The rule we consider is defined on a N-dimensional Hilbert space H N , and produces two biorthogonal bases of H N which are eigenstates of the Hamiltonians h=[Formula presented](q 2 +p 2 ), and of its adjoint h † . Here q and p are non-Hermitian operators obeying [q,p]=i(1−Nk), where k is a suitable orthogonal projection operator. These eigenstates are connected by ladder operators constructed out of q, p, q † and p † . Some examples are discussed.

AB - We propose a deformed version of the commutation rule introduced in 1967 by Buchdahl to describe a particular model of the truncated harmonic oscillator. The rule we consider is defined on a N-dimensional Hilbert space H N , and produces two biorthogonal bases of H N which are eigenstates of the Hamiltonians h=[Formula presented](q 2 +p 2 ), and of its adjoint h † . Here q and p are non-Hermitian operators obeying [q,p]=i(1−Nk), where k is a suitable orthogonal projection operator. These eigenstates are connected by ladder operators constructed out of q, p, q † and p † . Some examples are discussed.

UR - http://hdl.handle.net/10447/356741

M3 - Article

VL - 382

SP - 2526

EP - 2532

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

ER -